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Theorem feq23d 5220
 Description: Equality deduction for functions. (Contributed by set.mm contributors, 8-Jun-2013.)
Hypotheses
Ref Expression
feq23d.1 (φA = C)
feq23d.2 (φB = D)
Assertion
Ref Expression
feq23d (φ → (F:A–→BF:C–→D))

Proof of Theorem feq23d
StepHypRef Expression
1 feq23d.1 . 2 (φA = C)
2 feq23d.2 . 2 (φB = D)
3 feq23 5213 . 2 ((A = C B = D) → (F:A–→BF:C–→D))
41, 2, 3syl2anc 642 1 (φ → (F:A–→BF:C–→D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642  –→wf 4777 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-nan 1288  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-fn 4790  df-f 4791 This theorem is referenced by: (None)
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