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Mirrors > Home > ILE Home > Th. List > f1eq1 | Unicode version |
Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1eq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq1 5255 | . . 3 | |
2 | cnveq 4713 | . . . 4 | |
3 | 2 | funeqd 5145 | . . 3 |
4 | 1, 3 | anbi12d 464 | . 2 |
5 | df-f1 5128 | . 2 | |
6 | df-f1 5128 | . 2 | |
7 | 4, 5, 6 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 ccnv 4538 wfun 5117 wf 5119 wf1 5120 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 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-f1 5128 |
This theorem is referenced by: f1oeq1 5356 f1eq123d 5360 fun11iun 5388 fo00 5403 tposf12 6166 f1dom2g 6650 f1domg 6652 dom3d 6668 domtr 6679 djudom 6978 difinfsn 6985 djudoml 7075 djudomr 7076 |
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