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Theorem pm13.13a 43767
Description: One result of theorem *13.13 in [WhiteheadRussell] p. 178. A note on the section - to make the theorems more usable, and because inequality is notation for set theory (it is not defined in the predicate calculus section), this section will use classes instead of sets. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.13a ((𝜑𝑥 = 𝐴) → [𝐴 / 𝑥]𝜑)

Proof of Theorem pm13.13a
StepHypRef Expression
1 sbceq1a 3785 . 2 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21biimpac 478 1 ((𝜑𝑥 = 𝐴) → [𝐴 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395   = wceq 1534  [wsbc 3774
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-12 2164  ax-ext 2698
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-sbc 3775
This theorem is referenced by:  pm13.194  43772
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