ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  feq3d GIF version

Theorem feq3d 5336
Description: Equality deduction for functions. (Contributed by AV, 1-Jan-2020.)
Hypothesis
Ref Expression
feq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
feq3d (𝜑 → (𝐹:𝑋𝐴𝐹:𝑋𝐵))

Proof of Theorem feq3d
StepHypRef Expression
1 feq2d.1 . 2 (𝜑𝐴 = 𝐵)
2 feq3 5332 . 2 (𝐴 = 𝐵 → (𝐹:𝑋𝐴𝐹:𝑋𝐵))
31, 2syl 14 1 (𝜑 → (𝐹:𝑋𝐴𝐹:𝑋𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104   = wceq 1348  wf 5194
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-in 3127  df-ss 3134  df-f 5202
This theorem is referenced by:  uptx  13068  txcn  13069
  Copyright terms: Public domain W3C validator