Theorem ancom2s 566

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		pm3.22 265	. 2 |- ( ( ch /\ ps ) -> ( ps /\ ch ) )
2		an12s.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylan2 286	1 |- ( ( ph /\ ( ch /\ ps ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  an42s  589  ordsuc  4562  xpexr2m  5070  f1elima  5773  f1imaeq  5775  isosolem  5824  caovlem2d  6066  2ndconst  6222  isotilem  7004  prarloclem4  7496  mulsub  8357  leltadd  8403  eqord1  8439  divmul24ap  8672  fprodseq  11590  grpidpropdg  12792  cmnpropd  13096  unitpropdg  13315  blcomps  13866  blcom  13867  cxple  14307  cxple3  14311