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Mirrors > Home > ILE Home > Th. List > fneq12 | Unicode version |
Description: Equality theorem for function predicate with domain. (Contributed by Thierry Arnoux, 31-Jan-2017.) |
Ref | Expression |
---|---|
fneq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . 2 | |
2 | simpr 109 | . 2 | |
3 | 1, 2 | fneq12d 5264 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wfn 5167 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4028 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-fun 5174 df-fn 5175 |
This theorem is referenced by: tfrlem3ag 6258 tfrlem3a 6259 tfr1onlem3ag 6286 frecfnom 6350 |
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