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Theorem fveq1 5327
 Description: Equality theorem for function value. (Contributed by set.mm contributors, 29-Dec-1996.)
Assertion
Ref Expression
fveq1 (F = G → (FA) = (GA))

Proof of Theorem fveq1
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 breq 4641 . . 3 (F = G → (AFxAGx))
21iotabidv 4360 . 2 (F = G → (℩xAFx) = (℩xAGx))
3 df-fv 4795 . 2 (FA) = (℩xAFx)
4 df-fv 4795 . 2 (GA) = (℩xAGx)
52, 3, 43eqtr4g 2410 1 (F = G → (FA) = (GA))
 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
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