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Theorem sbcori 36275
Description: Distribution of class substitution over disjunction, in inference form. (Contributed by Giovanni Mascellani, 27-May-2019.)
Hypotheses
Ref Expression
sbcori.1 ([𝐴 / 𝑥]𝜑𝜒)
sbcori.2 ([𝐴 / 𝑥]𝜓𝜂)
Assertion
Ref Expression
sbcori ([𝐴 / 𝑥](𝜑𝜓) ↔ (𝜒𝜂))

Proof of Theorem sbcori
StepHypRef Expression
1 sbcor 3768 . 2 ([𝐴 / 𝑥](𝜑𝜓) ↔ ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓))
2 sbcori.1 . . 3 ([𝐴 / 𝑥]𝜑𝜒)
3 sbcori.2 . . 3 ([𝐴 / 𝑥]𝜓𝜂)
42, 3orbi12i 912 . 2 (([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓) ↔ (𝜒𝜂))
51, 4bitri 274 1 ([𝐴 / 𝑥](𝜑𝜓) ↔ (𝜒𝜂))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wo 844  [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-tru 1542  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3431  df-sbc 3716
This theorem is referenced by: (None)
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