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  4712  xpexr2m  5232  f1elima  5982  f1imaeq  5984  isosolem  6033  caovlem2d  6285  2ndconst  6462  isotilem  7352  prarloclem4  7871  mulsub  8735  leltadd  8782  eqord1  8818  divmul24ap  9054  fprodseq  12374  grpidpropdg  13752  cmnpropd  14187  unitpropdg  14563  blcomps  15639  blcom  15640  dvmptfsum  15968  cxple  16169  cxple3  16173  uhgr2edg  16669