ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sylan9req Structured version   GIF version

Theorem sylan9req 2090
Description: An equality transitivity deduction. (Contributed by NM, 23-Jun-2007.)
Hypotheses
Ref Expression
sylan9req.1 (φB = A)
sylan9req.2 (ψB = 𝐶)
Assertion
Ref Expression
sylan9req ((φ ψ) → A = 𝐶)

Proof of Theorem sylan9req
StepHypRef Expression
1 sylan9req.1 . . 3 (φB = A)
21eqcomd 2042 . 2 (φA = B)
3 sylan9req.2 . 2 (ψB = 𝐶)
42, 3sylan9eq 2089 1 ((φ ψ) → A = 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030
This theorem is referenced by:  xpid11m  4500  fndmu  4943  fodmrnu  5057  funcoeqres  5100  fvunsng  5300  prarloclem5  6483  addlocprlemeq  6516  zdiv  8104
  Copyright terms: Public domain W3C validator