Theorem 3jaoi

Description: Disjunction of three antecedents (inference). (Contributed by NM, 12-Sep-1995) (Proof shortened by Garrett Katz, 16-Jun-2026)

	Ref	Expression
Hypotheses	3jaoi.1	|- ( ph -> ps )
	3jaoi.2	|- ( ch -> ps )
	3jaoi.3	|- ( th -> ps )
Assertion	3jaoi	|- ( ( ph \/ ch \/ th ) -> ps )

Proof

Step	Hyp	Ref	Expression
1		3jaoi.1	|- ( ph -> ps )
2		3jaoi.2	|- ( ch -> ps )
3		3jaoi.3	|- ( th -> ps )
4		3jaob	|- ( ( ( ph \/ ch \/ th ) -> ps ) <-> ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) ) )
5	1 2 3 4	mpbir3an	|- ( ( ph \/ ch \/ th ) -> ps )