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Theorem pm13.181 2365
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 2117 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 pm13.18 2364 . 2 ((𝐵 = 𝐴𝐵𝐶) → 𝐴𝐶)
31, 2sylanb 280 1 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103   = wceq 1314  wne 2283
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-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2284
This theorem is referenced by:  fzprval  9802  mod2eq1n2dvds  11472
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