Metamath Proof Explorer


Theorem jaoian

Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005)

Ref Expression
Hypotheses jaoian.1 φψχ
jaoian.2 θψχ
Assertion jaoian φθψχ

Proof

Step Hyp Ref Expression
1 jaoian.1 φψχ
2 jaoian.2 θψχ
3 1 ex φψχ
4 2 ex θψχ
5 3 4 jaoi φθψχ
6 5 imp φθψχ