![]() |
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 5120 | . 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 1242 ‘cfv 4845 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-uni 3572 df-br 3756 df-iota 4810 df-fv 4853 |
This theorem is referenced by: fveq12d 5127 funssfv 5142 csbfv2g 5153 fvmptd 5196 fvmpt2d 5200 mpteqb 5204 fvmptt 5205 fmptco 5273 fvunsng 5300 fvsng 5302 fsnunfv 5306 f1ocnvfv1 5360 f1ocnvfv2 5361 fcof1 5366 fcofo 5367 fnofval 5663 offval2 5668 ofrfval2 5669 caofinvl 5675 tfrlemi1 5887 rdg0g 5915 freceq1 5919 oav 5973 omv 5974 oeiv 5975 fseq1p1m1 8726 iseqeq3 8896 expival 8911 |
Copyright terms: Public domain | W3C validator |