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Theorem pm13.13b 37631
 Description: Theorem *13.13 in [WhiteheadRussell] p. 178 with different variable substitution. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.13b (([𝐴 / 𝑥]𝜑𝑥 = 𝐴) → 𝜑)

Proof of Theorem pm13.13b
StepHypRef Expression
1 sbceq1a 3413 . 2 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21biimparc 503 1 (([𝐴 / 𝑥]𝜑𝑥 = 𝐴) → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   = wceq 1475  [wsbc 3402 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-sbc 3403 This theorem is referenced by:  pm14.24  37655
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