Theorem ancom2s 534

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Hypothesis

Ref	Expression
an12s.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

Ref	Expression
ancom2s	|- ( ( ph /\ ( ch /\ ps ) ) -> th )

Proof of Theorem ancom2s

Step	Hyp	Ref	Expression
1		pm3.22 262	. 2 |- ( ( ch /\ ps ) -> ( ps /\ ch ) )
2		an12s.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylan2 281	1 |- ( ( ph /\ ( ch /\ ps ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  an42s  557  ordsuc  4392  xpexr2m  4885  f1elima  5566  f1imaeq  5568  isosolem  5617  caovlem2d  5851  2ndconst  6001  isotilem  6755  prarloclem4  7118  mulsub  7940  leltadd  7986  eqord1  8022  divmul24ap  8244