ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  feq2d GIF version

Theorem feq2d 5368
Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
feq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
feq2d (𝜑 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))

Proof of Theorem feq2d
StepHypRef Expression
1 feq2d.1 . 2 (𝜑𝐴 = 𝐵)
2 feq2 5364 . 2 (𝐴 = 𝐵 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105   = wceq 1364  wf 5227
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-4 1521  ax-17 1537  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-fn 5234  df-f 5235
This theorem is referenced by:  feq12d  5370  ffdm  5401  fsng  5705  issmo2  6308  qliftf  6638  elpm2r  6684  casef  7105  fseq1p1m1  10112  fseq1m1p1  10113  seqf  10479  seqf2  10482  intopsn  12809  resmhm  12905  isghm  13143  resghm  13160  lmtopcnp  14147  ellimc3apf  14526  dvidlemap  14557  dviaddf  14566  dvimulf  14567  dvcjbr  14569  dvcj  14570  dvrecap  14574  dvmptclx  14577
  Copyright terms: Public domain W3C validator