NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  pm13.181 GIF version

Theorem pm13.181 2589
Description: Theorem *13.181 in [WhiteheadRussell] p. 178. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.181 ((A = B BC) → AC)

Proof of Theorem pm13.181
StepHypRef Expression
1 eqcom 2355 . 2 (A = BB = A)
2 pm13.18 2588 . 2 ((B = A BC) → AC)
31, 2sylanb 458 1 ((A = B BC) → AC)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   = wceq 1642  wne 2516
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-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-ne 2518
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator