Theorem ancom2s 572

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 )

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 theorem is used by:  an42s  597  ordsuc  4710  xpexr2m  5229  f1elima  5979  f1imaeq  5981  isosolem  6030  caovlem2d  6282  2ndconst  6458  isotilem  7347  prarloclem4  7866  mulsub  8730  leltadd  8777  eqord1  8813  divmul24ap  9049  fprodseq  12369  grpidpropdg  13747  cmnpropd  14182  unitpropdg  14539  blcomps  15588  blcom  15589  dvmptfsum  15917  cxple  16114  cxple3  16118  uhgr2edg  16613