Theorem 4an4132

Description: A rearrangement of conjuncts for a 4-right-nested conjunction. (Contributed by Alan Sare, 30-May-2018)

	Ref	Expression
Hypothesis	4an4132.1	|- ( ( ( ( th /\ ch ) /\ ps ) /\ ph ) -> ta )
Assertion	4an4132	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		4an4132.1	|- ( ( ( ( th /\ ch ) /\ ps ) /\ ph ) -> ta )
2		simpr	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> th )
3		simplr	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ch )
4	2 3	jca	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ( th /\ ch ) )
5		simpllr	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ps )
6		simplll	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ph )
7	4 5 6 1	syl21anc	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )