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Mirrors > Home > ILE Home > Th. List > fneq1 | Unicode version |
Description: Equality theorem for function predicate with domain. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
fneq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funeq 5113 | . . 3 | |
2 | dmeq 4709 | . . . 4 | |
3 | 2 | eqeq1d 2126 | . . 3 |
4 | 1, 3 | anbi12d 464 | . 2 |
5 | df-fn 5096 | . 2 | |
6 | df-fn 5096 | . 2 | |
7 | 4, 5, 6 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 cdm 4509 wfun 5087 wfn 5088 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-fun 5095 df-fn 5096 |
This theorem is referenced by: fneq1d 5183 fneq1i 5187 fn0 5212 feq1 5225 foeq1 5311 f1ocnv 5348 mpteqb 5479 eufnfv 5616 tfr0dm 6187 tfrlemiex 6196 tfr1onlemsucfn 6205 tfr1onlemsucaccv 6206 tfr1onlembxssdm 6208 tfr1onlembfn 6209 tfr1onlemex 6212 tfr1onlemaccex 6213 tfr1onlemres 6214 mapval2 6540 elixp2 6564 ixpfn 6566 elixpsn 6597 |
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