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Theorem pm13.181 3021
Description: Theorem *13.181 in [WhiteheadRussell] p. 178. (Contributed by Andrew Salmon, 3-Jun-2011.) (Proof shortened by Wolf Lammen, 30-Oct-2024.)
Assertion
Ref Expression
pm13.181 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)

Proof of Theorem pm13.181
StepHypRef Expression
1 neeq1 3001 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
21biimpar 477 1 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395   = wceq 1537  wne 2938
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-cleq 2727  df-ne 2939
This theorem is referenced by:  fzprval  13622  frgrwopreglem5a  30340  ax6e2ndeqALT  44929
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