Theorem mpsyl4anc

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypotheses	mpsyl4anc.1	|- ph
	mpsyl4anc.2	|- ps
	mpsyl4anc.3	|- ch
	mpsyl4anc.4	|- ( th -> ta )
	mpsyl4anc.5	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ ta ) -> et )
Assertion	mpsyl4anc	|- ( th -> et )

Proof

Step	Hyp	Ref	Expression
1		mpsyl4anc.1	|- ph
2		mpsyl4anc.2	|- ps
3		mpsyl4anc.3	|- ch
4		mpsyl4anc.4	|- ( th -> ta )
5		mpsyl4anc.5	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ ta ) -> et )
6	1	a1i	|- ( th -> ph )
7	2	a1i	|- ( th -> ps )
8	3	a1i	|- ( th -> ch )
9	6 7 8 4 5	syl1111anc	|- ( th -> et )