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Theorem pm13.181 2905
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 2658 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 pm13.18 2904 . 2 ((𝐵 = 𝐴𝐵𝐶) → 𝐴𝐶)
31, 2sylanb 488 1 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383   = wceq 1523  wne 2823
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745  df-cleq 2644  df-ne 2824
This theorem is referenced by:  fzprval  12439  frgrwopreglem5a  27291  ax6e2ndeqALT  39481
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