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  4600  xpexr2m  5112  f1elima  5823  f1imaeq  5825  isosolem  5874  caovlem2d  6120  2ndconst  6289  isotilem  7081  prarloclem4  7584  mulsub  8446  leltadd  8493  eqord1  8529  divmul24ap  8762  fprodseq  11767  grpidpropdg  13078  cmnpropd  13503  unitpropdg  13782  blcomps  14718  blcom  14719  dvmptfsum  15047  cxple  15239  cxple3  15243