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Mirrors > Home > ILE Home > Th. List > funeq | Unicode version |
Description: Equality theorem for function predicate. (Contributed by NM, 16-Aug-1994.) |
Ref | Expression |
---|---|
funeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3052 | . . 3 | |
2 | funss 4940 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | eqimss 3051 | . . 3 | |
5 | funss 4940 | . . 3 | |
6 | 4, 5 | syl 14 | . 2 |
7 | 3, 6 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wss 2973 wfun 4916 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-in 2979 df-ss 2986 df-br 3786 df-opab 3840 df-rel 4370 df-cnv 4371 df-co 4372 df-fun 4924 |
This theorem is referenced by: funeqi 4942 funeqd 4943 fununi 4987 funcnvuni 4988 cnvresid 4993 fneq1 5007 fundmeng 6310 |
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