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Theorem sbciedOLD 3761
Description: Obsolete version of sbcied 3760 as of 12-Oct-2024. (Contributed by NM, 13-Dec-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
sbciedOLD.1 (𝜑𝐴𝑉)
sbciedOLD.2 ((𝜑𝑥 = 𝐴) → (𝜓𝜒))
Assertion
Ref Expression
sbciedOLD (𝜑 → ([𝐴 / 𝑥]𝜓𝜒))
Distinct variable groups:   𝑥,𝐴   𝜑,𝑥   𝜒,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝑉(𝑥)

Proof of Theorem sbciedOLD
StepHypRef Expression
1 sbciedOLD.1 . 2 (𝜑𝐴𝑉)
2 sbciedOLD.2 . 2 ((𝜑𝑥 = 𝐴) → (𝜓𝜒))
3 nfv 1917 . 2 𝑥𝜑
4 nfvd 1918 . 2 (𝜑 → Ⅎ𝑥𝜒)
51, 2, 3, 4sbciedf 3759 1 (𝜑 → ([𝐴 / 𝑥]𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396   = 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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