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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 5030 | . . 3 | |
2 | cnveq 4509 | . . . 4 | |
3 | 2 | funeqd 4923 | . . 3 |
4 | 1, 3 | anbi12d 442 | . 2 |
5 | df-f1 4907 | . 2 | |
6 | df-f1 4907 | . 2 | |
7 | 4, 5, 6 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 ccnv 4344 wfun 4896 wf 4898 wf1 4899 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 |
This theorem is referenced by: f1oeq1 5117 f1eq123d 5121 fun11iun 5147 fo00 5162 tposf12 5884 f1dom2g 6236 f1domg 6238 dom3d 6254 domtr 6265 |
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