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Theorem pm13.181 2331
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 2085 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 pm13.18 2330 . 2 ((𝐵 = 𝐴𝐵𝐶) → 𝐴𝐶)
31, 2sylanb 278 1 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102   = wceq 1285  wne 2249
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  fzprval  9211  mod2eq1n2dvds  10470
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