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Theorem pm13.13b 42780
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 3754 . 2 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21biimparc 481 1 (([𝐴 / 𝑥]𝜑𝑥 = 𝐴) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397   = wceq 1542  [wsbc 3743
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-sbc 3744
This theorem is referenced by:  pm14.24  42804
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