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Mirrors > Home > ILE Home > Th. List > foun | Unicode version |
Description: The union of two onto functions with disjoint domains is an onto function. (Contributed by Mario Carneiro, 22-Jun-2016.) |
Ref | Expression |
---|---|
foun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fofn 5128 | . . . 4 | |
2 | fofn 5128 | . . . 4 | |
3 | 1, 2 | anim12i 331 | . . 3 |
4 | fnun 5025 | . . 3 | |
5 | 3, 4 | sylan 277 | . 2 |
6 | rnun 4752 | . . 3 | |
7 | forn 5129 | . . . . 5 | |
8 | 7 | ad2antrr 471 | . . . 4 |
9 | forn 5129 | . . . . 5 | |
10 | 9 | ad2antlr 472 | . . . 4 |
11 | 8, 10 | uneq12d 3127 | . . 3 |
12 | 6, 11 | syl5eq 2125 | . 2 |
13 | df-fo 4928 | . 2 | |
14 | 5, 12, 13 | sylanbrc 408 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 cun 2971 cin 2972 c0 3251 crn 4364 wfn 4917 wfo 4920 |
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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 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-v 2603 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-br 3786 df-opab 3840 df-id 4048 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-fun 4924 df-fn 4925 df-f 4926 df-fo 4928 |
This theorem is referenced by: (None) |
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