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  591  ordsuc  4659  xpexr2m  5176  f1elima  5909  f1imaeq  5911  isosolem  5960  caovlem2d  6210  2ndconst  6382  isotilem  7196  prarloclem4  7708  mulsub  8570  leltadd  8617  eqord1  8653  divmul24ap  8886  fprodseq  12134  grpidpropdg  13447  cmnpropd  13872  unitpropdg  14152  blcomps  15110  blcom  15111  dvmptfsum  15439  cxple  15631  cxple3  15635  uhgr2edg  16045