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Mirrors > Home > ILE Home > Th. List > f1oabexg | Unicode version |
Description: The class of all 1-1-onto functions mapping one set to another is a set. (Contributed by Paul Chapman, 25-Feb-2008.) |
Ref | Expression |
---|---|
f1oabexg.1 |
Ref | Expression |
---|---|
f1oabexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oabexg.1 | . 2 | |
2 | f1of 5367 | . . . . 5 | |
3 | 2 | anim1i 338 | . . . 4 |
4 | 3 | ss2abi 3169 | . . 3 |
5 | eqid 2139 | . . . 4 | |
6 | 5 | fabexg 5310 | . . 3 |
7 | ssexg 4067 | . . 3 | |
8 | 4, 6, 7 | sylancr 410 | . 2 |
9 | 1, 8 | eqeltrid 2226 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 cab 2125 cvv 2686 wss 3071 wf 5119 wf1o 5122 |
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-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-13 1491 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 ax-un 4355 |
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-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-xp 4545 df-rel 4546 df-cnv 4547 df-dm 4549 df-rn 4550 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-f1o 5130 |
This theorem is referenced by: (None) |
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