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Mirrors > Home > ILE Home > Th. List > opabex | Unicode version |
Description: Existence of a function expressed as class of ordered pairs. (Contributed by NM, 21-Jul-1996.) |
Ref | Expression |
---|---|
opabex.1 | |
opabex.2 |
Ref | Expression |
---|---|
opabex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funopab 4955 | . . 3 | |
2 | opabex.2 | . . . 4 | |
3 | moanimv 2016 | . . . 4 | |
4 | 2, 3 | mpbir 144 | . . 3 |
5 | 1, 4 | mpgbir 1382 | . 2 |
6 | opabex.1 | . . 3 | |
7 | dmopabss 4565 | . . 3 | |
8 | 6, 7 | ssexi 3916 | . 2 |
9 | funex 5405 | . 2 | |
10 | 5, 8, 9 | mp2an 416 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wcel 1433 wmo 1942 cvv 2601 copab 3838 cdm 4363 wfun 4916 |
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-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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-coll 3893 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 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-ral 2353 df-rex 2354 df-reu 2355 df-rab 2357 df-v 2603 df-sbc 2816 df-csb 2909 df-un 2977 df-in 2979 df-ss 2986 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-f1 4927 df-fo 4928 df-f1o 4929 df-fv 4930 |
This theorem is referenced by: (None) |
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