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Theorem pm13.13b 39129
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 3587 . 2 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21biimparc 505 1 (([𝐴 / 𝑥]𝜑𝑥 = 𝐴) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383   = wceq 1632  [wsbc 3576
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-12 2196  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-sbc 3577
This theorem is referenced by:  pm14.24  39153
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