![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > idahom | Structured version Unicode version |
Description: Domain and codomain of the identity arrow. (Contributed by Mario Carneiro, 11-Jan-2017.) |
Ref | Expression |
---|---|
idafval.i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
idafval.b |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
idafval.c |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
idahom.x |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
idahom.h |
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
idahom |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idafval.i |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | idafval.b |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | idafval.c |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | eqid 2454 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | idahom.x |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 1, 2, 3, 4, 5 | idaval 15049 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | idahom.h |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | eqid 2454 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 2, 8, 4, 3, 5 | catidcl 14743 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 7, 2, 3, 8, 5, 5, 9 | elhomai2 15025 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 6, 10 | eqeltrd 2542 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-rep 4514 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 ax-un 6485 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-reu 2806 df-rmo 2807 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3399 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-op 3995 df-ot 3997 df-uni 4203 df-iun 4284 df-br 4404 df-opab 4462 df-mpt 4463 df-id 4747 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-res 4963 df-ima 4964 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-f1 5534 df-fo 5535 df-f1o 5536 df-fv 5537 df-riota 6164 df-ov 6206 df-cat 14729 df-cid 14730 df-homa 15017 df-ida 15046 |
This theorem is referenced by: idadm 15052 idacd 15053 idaf 15054 arwlid 15063 arwrid 15064 |
Copyright terms: Public domain | W3C validator |