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Theorem sbcori 38116
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 3839 . 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 915 . 2 (([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓) ↔ (𝜒𝜂))
51, 4bitri 275 1 ([𝐴 / 𝑥](𝜑𝜓) ↔ (𝜒𝜂))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wo 848  [wsbc 3788
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-sbc 3789
This theorem is referenced by: (None)
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