![]() |
Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > elpadd2at | Structured version Visualization version Unicode version |
Description: Membership in a projective subspace sum of two points. (Contributed by NM, 29-Jan-2012.) |
Ref | Expression |
---|---|
paddfval.l |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
paddfval.j |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
paddfval.a |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
paddfval.p |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
elpadd2at |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 1009 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | simp2 1010 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | snssd 4085 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | simp3 1011 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | snnzg 4057 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 5 | 3ad2ant2 1031 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | paddfval.l |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | paddfval.j |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | paddfval.a |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | paddfval.p |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 7, 8, 9, 10 | elpaddat 33370 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 1, 3, 4, 6, 11 | syl31anc 1274 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | oveq1 6282 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 13 | breq2d 4385 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 14 | rexsng 3974 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | 3ad2ant2 1031 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 16 | anbi2d 715 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 12, 17 | bitrd 261 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-8 1892 ax-9 1899 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 ax-rep 4486 ax-sep 4496 ax-nul 4505 ax-pow 4553 ax-pr 4611 ax-un 6570 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2623 df-ral 2741 df-rex 2742 df-reu 2743 df-rab 2745 df-v 3014 df-sbc 3235 df-csb 3331 df-dif 3374 df-un 3376 df-in 3378 df-ss 3385 df-nul 3699 df-if 3849 df-pw 3920 df-sn 3936 df-pr 3938 df-op 3942 df-uni 4168 df-iun 4249 df-br 4374 df-opab 4433 df-mpt 4434 df-id 4726 df-xp 4817 df-rel 4818 df-cnv 4819 df-co 4820 df-dm 4821 df-rn 4822 df-res 4823 df-ima 4824 df-iota 5524 df-fun 5562 df-fn 5563 df-f 5564 df-f1 5565 df-fo 5566 df-f1o 5567 df-fv 5568 df-riota 6237 df-ov 6278 df-oprab 6279 df-mpt2 6280 df-1st 6780 df-2nd 6781 df-lub 16230 df-join 16232 df-lat 16302 df-ats 32834 df-padd 33362 |
This theorem is referenced by: elpadd2at2 33373 |
Copyright terms: Public domain | W3C validator |