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Theorem fveq1d 5330
Description: Equality deduction for function value. (Contributed by set.mm contributors, 2-Sep-2003.)
Hypothesis
Ref Expression
fveq1d.1 (φF = G)
Assertion
Ref Expression
fveq1d (φ → (FA) = (GA))

Proof of Theorem fveq1d
StepHypRef Expression
1 fveq1d.1 . 2 (φF = G)
2 fveq1 5327 . 2 (F = G → (FA) = (GA))
31, 2syl 15 1 (φ → (FA) = (GA))
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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