![]() |
Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > Mathboxes > pr01ssre | Structured version Unicode version |
Description: The range of the
indicator function is a subset of ![]() |
Ref | Expression |
---|---|
pr01ssre |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 9492 |
. 2
![]() ![]() ![]() ![]() | |
2 | 1re 9491 |
. 2
![]() ![]() ![]() ![]() | |
3 | prssi 4132 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | mp2an 672 |
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-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 ax-1cn 9446 ax-icn 9447 ax-addcl 9448 ax-addrcl 9449 ax-mulcl 9450 ax-mulrcl 9451 ax-i2m1 9456 ax-1ne0 9457 ax-rnegex 9459 ax-rrecex 9460 ax-cnre 9461 |
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-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ne 2647 df-ral 2801 df-rex 2802 df-rab 2805 df-v 3074 df-dif 3434 df-un 3436 df-in 3438 df-ss 3445 df-nul 3741 df-if 3895 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4195 df-br 4396 df-iota 5484 df-fv 5529 df-ov 6198 |
This theorem is referenced by: indsum 26619 |
Copyright terms: Public domain | W3C validator |