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Theorem sbcori 34143
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 3585 . 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 544 . 2 (([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓) ↔ (𝜒𝜂))
51, 4bitri 264 1 ([𝐴 / 𝑥](𝜑𝜓) ↔ (𝜒𝜂))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wo 382  [wsbc 3541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-12 2160  ax-13 2355  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-v 3306  df-sbc 3542
This theorem is referenced by: (None)
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