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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 5422 | . . . 4 | |
2 | fofn 5422 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | fnun 5304 | . . 3 | |
5 | 3, 4 | sylan 281 | . 2 |
6 | rnun 5019 | . . 3 | |
7 | forn 5423 | . . . . 5 | |
8 | 7 | ad2antrr 485 | . . . 4 |
9 | forn 5423 | . . . . 5 | |
10 | 9 | ad2antlr 486 | . . . 4 |
11 | 8, 10 | uneq12d 3282 | . . 3 |
12 | 6, 11 | eqtrid 2215 | . 2 |
13 | df-fo 5204 | . 2 | |
14 | 5, 12, 13 | sylanbrc 415 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 cun 3119 cin 3120 c0 3414 crn 4612 wfn 5193 wfo 5196 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-id 4278 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-fun 5200 df-fn 5201 df-f 5202 df-fo 5204 |
This theorem is referenced by: (None) |
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