![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > fveq1d | GIF version |
Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003.) |
Ref | Expression |
---|---|
fveq1d.1 | ⊢ (𝜑 → 𝐹 = 𝐺) |
Ref | Expression |
---|---|
fveq1d | ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1d.1 | . 2 ⊢ (𝜑 → 𝐹 = 𝐺) | |
2 | fveq1 5229 | . 2 ⊢ (𝐹 = 𝐺 → (𝐹‘𝐴) = (𝐺‘𝐴)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (𝐹‘𝐴) = (𝐺‘𝐴)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1285 ‘cfv 4952 |
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 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-rex 2359 df-uni 3622 df-br 3806 df-iota 4917 df-fv 4960 |
This theorem is referenced by: fveq12d 5236 funssfv 5252 csbfv2g 5263 fvmptd 5306 fvmpt2d 5310 mpteqb 5314 fvmptt 5315 fmptco 5383 fvunsng 5410 fvsng 5412 fsnunfv 5416 f1ocnvfv1 5469 f1ocnvfv2 5470 fcof1 5475 fcofo 5476 fnofval 5773 offval2 5778 ofrfval2 5779 caofinvl 5785 tfrlemi1 6002 rdg0g 6058 freceq1 6062 oav 6119 omv 6120 oeiv 6121 fseq1p1m1 9257 iseqeq3 9596 iseqid 9633 iseqz 9636 serige0 9640 serile 9641 expival 9645 ibcval5 9857 bcn2 9858 shftcan1 9941 shftcan2 9942 shftvalg 9943 shftval4g 9944 climshft2 10364 iserile 10399 sumeq2d 10415 sumeq2 10416 |
Copyright terms: Public domain | W3C validator |