Theorem ancom2s 568

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  593  ordsuc  4690  xpexr2m  5209  f1elima  5952  f1imaeq  5954  isosolem  6003  caovlem2d  6255  2ndconst  6431  isotilem  7310  prarloclem4  7829  mulsub  8691  leltadd  8738  eqord1  8774  divmul24ap  9007  fprodseq  12294  grpidpropdg  13637  cmnpropd  14048  unitpropdg  14393  blcomps  15387  blcom  15388  dvmptfsum  15716  cxple  15908  cxple3  15912  uhgr2edg  16327