Metamath Proof Explorer


Theorem sbcori

Description: Distribution of class substitution over disjunction, in inference form. (Contributed by Giovanni Mascellani, 27-May-2019)

Ref Expression
Hypotheses sbcori.1 [˙A / x]˙ φ χ
sbcori.2 [˙A / x]˙ ψ η
Assertion sbcori [˙A / x]˙ φ ψ χ η

Proof

Step Hyp Ref Expression
1 sbcori.1 [˙A / x]˙ φ χ
2 sbcori.2 [˙A / x]˙ ψ η
3 sbcor [˙A / x]˙ φ ψ [˙A / x]˙ φ [˙A / x]˙ ψ
4 1 2 orbi12i [˙A / x]˙ φ [˙A / x]˙ ψ χ η
5 3 4 bitri [˙A / x]˙ φ ψ χ η