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Mirrors > Home > NFE Home > Th. List > fveq1d | GIF version |
Description: Equality deduction for function value. (Contributed by set.mm contributors, 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 5327 | . 2 ⊢ (F = G → (F ‘A) = (G ‘A)) | |
3 | 1, 2 | syl 15 | 1 ⊢ (φ → (F ‘A) = (G ‘A)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1642 ‘cfv 4781 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-uni 3892 df-iota 4339 df-br 4640 df-fv 4795 |
This theorem is referenced by: fveq12d 5333 csbfv2g 5337 funssfv 5343 fvunsn 5444 fvsng 5446 f1ocnvfv1 5476 fvmptd 5702 |
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