Theorem anass1rs 577

Description: Commutative-associative law for conjunction in an antecedent. (Contributed by Jeff Madsen, 19-Jun-2011.)

Hypothesis

Ref	Expression
anass1rs.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

Ref	Expression
anass1rs	|- ( ( ( ph /\ ch ) /\ ps ) -> th )

Proof of Theorem anass1rs

Step	Hyp	Ref	Expression
1		anass1rs.1	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
2	1	anassrs 404	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	2	an32s 574	1 |- ( ( ( ph /\ ch ) /\ ps ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  ifeqeqxdc  3687  creui  9290  qreccl  10042  grppropd  13822  grpinvpropdg  13880  ringrghm  14367