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Theorem pm13.13b 37430
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 3408 . 2 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21biimparc 502 1 (([𝐴 / 𝑥]𝜑𝑥 = 𝐴) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382   = wceq 1474  [wsbc 3397
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-12 2031  ax-ext 2585
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-sb 1866  df-clab 2592  df-cleq 2598  df-clel 2601  df-sbc 3398
This theorem is referenced by:  pm14.24  37454
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