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Mirrors > Home > ILE Home > Th. List > f1oeq1 | Unicode version |
Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1oeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq1 5318 | . . 3 | |
2 | foeq1 5336 | . . 3 | |
3 | 1, 2 | anbi12d 464 | . 2 |
4 | df-f1o 5125 | . 2 | |
5 | df-f1o 5125 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wf1 5115 wfo 5116 wf1o 5117 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 |
This theorem is referenced by: f1oeq123d 5357 f1ocnvb 5374 f1orescnv 5376 f1ovi 5399 f1osng 5401 f1oresrab 5578 fsn 5585 isoeq1 5695 mapsn 6577 mapsnf1o3 6584 f1oen3g 6641 ensn1 6683 xpcomf1o 6712 xpen 6732 seq3f1olemstep 10267 seq3f1olemp 10268 fihasheqf1oi 10527 fihashf1rn 10528 hashfacen 10572 summodc 11145 fsum3 11149 |
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