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Theorem sbciegOLD 3756
Description: Obsolete version of sbcieg 3755 as of 12-Oct-2024. (Contributed by NM, 10-Nov-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
sbciegOLD.1 (𝑥 = 𝐴 → (𝜑𝜓))
Assertion
Ref Expression
sbciegOLD (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜓))
Distinct variable groups:   𝑥,𝐴   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝑉(𝑥)

Proof of Theorem sbciegOLD
StepHypRef Expression
1 nfv 1917 . 2 𝑥𝜓
2 sbciegOLD.1 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
31, 2sbciegf 3754 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1539  wcel 2106  [wsbc 3715
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-12 2171  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-sbc 3716
This theorem is referenced by: (None)
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