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Mirrors > Home > ILE Home > Th. List > feq123 | Unicode version |
Description: Equality theorem for functions. (Contributed by FL, 16-Nov-2008.) |
Ref | Expression |
---|---|
feq123 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 981 | . 2 | |
2 | simp2 982 | . 2 | |
3 | simp3 983 | . 2 | |
4 | 1, 2, 3 | feq123d 5263 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wceq 1331 wf 5119 |
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 |
This theorem is referenced by: (None) |
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