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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 5347 | . . . 4 | |
2 | fofn 5347 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | fnun 5229 | . . 3 | |
5 | 3, 4 | sylan 281 | . 2 |
6 | rnun 4947 | . . 3 | |
7 | forn 5348 | . . . . 5 | |
8 | 7 | ad2antrr 479 | . . . 4 |
9 | forn 5348 | . . . . 5 | |
10 | 9 | ad2antlr 480 | . . . 4 |
11 | 8, 10 | uneq12d 3231 | . . 3 |
12 | 6, 11 | syl5eq 2184 | . 2 |
13 | df-fo 5129 | . 2 | |
14 | 5, 12, 13 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 cun 3069 cin 3070 c0 3363 crn 4540 wfn 5118 wfo 5121 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-id 4215 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-fun 5125 df-fn 5126 df-f 5127 df-fo 5129 |
This theorem is referenced by: (None) |
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