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Theorem pm13.13a 37527
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 3317 . 2 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21biimpac 501 1 ((𝜑𝑥 = 𝐴) → [𝐴 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382   = wceq 1474  [wsbc 3306
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-12 1983  ax-ext 2494
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-sb 1831  df-clab 2501  df-cleq 2507  df-clel 2510  df-sbc 3307
This theorem is referenced by:  pm13.194  37532
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