Theorem 3impcombi

Description: A 1-hypothesis propositional calculus deduction. (Contributed by Alan Sare, 25-Sep-2017)

	Ref	Expression
Hypothesis	3impcombi.1	|- ( ( ph /\ ps /\ ph ) -> ( ch <-> th ) )
Assertion	3impcombi	|- ( ( ps /\ ph /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		3impcombi.1	|- ( ( ph /\ ps /\ ph ) -> ( ch <-> th ) )
2	1	biimpd	|- ( ( ph /\ ps /\ ph ) -> ( ch -> th ) )
3	2	3anidm13	|- ( ( ph /\ ps ) -> ( ch -> th ) )
4	3	ancoms	|- ( ( ps /\ ph ) -> ( ch -> th ) )
5	4	3impia	|- ( ( ps /\ ph /\ ch ) -> th )