ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm13.181 GIF version

Theorem pm13.181 2287
Description: Theorem *13.181 in [WhiteheadRussell] p. 178. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.181 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)

Proof of Theorem pm13.181
StepHypRef Expression
1 eqcom 2042 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 pm13.18 2286 . 2 ((𝐵 = 𝐴𝐵𝐶) → 𝐴𝐶)
31, 2sylanb 268 1 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97   = wceq 1243  wne 2204
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-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206
This theorem is referenced by:  fzprval  8944
  Copyright terms: Public domain W3C validator