Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > tpossym | Unicode version |
Description: Two ways to say a function is symmetric. (Contributed by Mario Carneiro, 4-Oct-2015.) |
Ref | Expression |
---|---|
tpossym | tpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tposfn 5911 | . . 3 tpos | |
2 | eqfnov2 5628 | . . 3 tpos tpos tpos | |
3 | 1, 2 | mpancom 413 | . 2 tpos tpos |
4 | eqcom 2083 | . . . 4 tpos tpos | |
5 | vex 2604 | . . . . . 6 | |
6 | vex 2604 | . . . . . 6 | |
7 | ovtposg 5897 | . . . . . 6 tpos | |
8 | 5, 6, 7 | mp2an 416 | . . . . 5 tpos |
9 | 8 | eqeq2i 2091 | . . . 4 tpos |
10 | 4, 9 | bitri 182 | . . 3 tpos |
11 | 10 | 2ralbii 2374 | . 2 tpos |
12 | 3, 11 | syl6bb 194 | 1 tpos |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wcel 1433 wral 2348 cvv 2601 cxp 4361 wfn 4917 (class class class)co 5532 tpos ctpos 5882 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-nul 3904 ax-pow 3948 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-sbc 2816 df-csb 2909 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-iun 3680 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-fo 4928 df-fv 4930 df-ov 5535 df-tpos 5883 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |