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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 5138 | . . 3 | |
2 | dmeq 4734 | . . . 4 | |
3 | 2 | eqeq1d 2146 | . . 3 |
4 | 1, 3 | anbi12d 464 | . 2 |
5 | df-fn 5121 | . 2 | |
6 | df-fn 5121 | . 2 | |
7 | 4, 5, 6 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 cdm 4534 wfun 5112 wfn 5113 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-fun 5120 df-fn 5121 |
This theorem is referenced by: fneq1d 5208 fneq1i 5212 fn0 5237 feq1 5250 foeq1 5336 f1ocnv 5373 mpteqb 5504 eufnfv 5641 tfr0dm 6212 tfrlemiex 6221 tfr1onlemsucfn 6230 tfr1onlemsucaccv 6231 tfr1onlembxssdm 6233 tfr1onlembfn 6234 tfr1onlemex 6237 tfr1onlemaccex 6238 tfr1onlemres 6239 mapval2 6565 elixp2 6589 ixpfn 6591 elixpsn 6622 |
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