Theorem ancom2s 530

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		pm3.22 261	. 2 |- ( ( ch /\ ps ) -> ( ps /\ ch ) )
2		an12s.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylan2 280	1 |- ( ( ph /\ ( ch /\ ps ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  an42s  553  ordsuc  4306  xpexr2m  4782  f1elima  5433  f1imaeq  5435  isosolem  5483  caovlem2d  5713  2ndconst  5863  isotilem  6419  prarloclem4  6688  mulsub  7505  leltadd  7551  divmul24ap  7804