Theorem 4an4132 38705

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

Hypothesis

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

Assertion

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

Proof of Theorem 4an4132

Step	Hyp	Ref	Expression
1		simpr 477	. . 3 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> th )
2		simplr 792	. . 3 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ch )
3	1, 2	jca 554	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ( th /\ ch ) )
4		simpllr 799	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ps )
5		simplll 798	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ph )
6		4an4132.1	. 2 |- ( ( ( ( th /\ ch ) /\ ps ) /\ ph ) -> ta )
7	3, 4, 5, 6	syl21anc 1325	1 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  sineq0ALT  39173