Theorem impel

Description: An inference for implication elimination. (Contributed by Giovanni Mascellani, 23-May-2019) (Proof shortened by Wolf Lammen, 2-Sep-2020)

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

Proof

Step	Hyp	Ref	Expression
1		impel.1	|- ( ph -> ( ps -> ch ) )
2		impel.2	|- ( th -> ps )
3	2 1	syl5	|- ( ph -> ( th -> ch ) )
4	3	imp	|- ( ( ph /\ th ) -> ch )