Theorem 4an31 38704

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

Hypothesis

Ref	Expression
4an31.1	|- ( ( ( ( ch /\ ps ) /\ ph ) /\ th ) -> ta )

Assertion

Ref	Expression
4an31	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Proof of Theorem 4an31

Step	Hyp	Ref	Expression
1		an31 841	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ch /\ ps ) /\ ph ) )
2		4an31.1	. 2 |- ( ( ( ( ch /\ ps ) /\ ph ) /\ th ) -> ta )
3	1, 2	sylanb 489	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