New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > fveq1 | GIF version |
Description: Equality theorem for function value. (Contributed by set.mm contributors, 29-Dec-1996.) |
Ref | Expression |
---|---|
fveq1 | ⊢ (F = G → (F ‘A) = (G ‘A)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 4641 | . . 3 ⊢ (F = G → (AFx ↔ AGx)) | |
2 | 1 | iotabidv 4360 | . 2 ⊢ (F = G → (℩xAFx) = (℩xAGx)) |
3 | df-fv 4795 | . 2 ⊢ (F ‘A) = (℩xAFx) | |
4 | df-fv 4795 | . 2 ⊢ (G ‘A) = (℩xAGx) | |
5 | 2, 3, 4 | 3eqtr4g 2410 | 1 ⊢ (F = G → (F ‘A) = (G ‘A)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1642 ℩cio 4337 class class class wbr 4639 ‘cfv 4781 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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: fveq1i 5329 fveq1d 5330 eqfnfv 5392 isoeq1 5482 oveq 5529 |
Copyright terms: Public domain | W3C validator |