Theorem an4s 799

Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995.)

Hypothesis

Ref	Expression
an4s.1	|- (((ph /\ ps) /\ (ch /\ th)) -> ta)

Assertion

Ref	Expression
an4s	|- (((ph /\ ch) /\ (ps /\ th)) -> ta)

Proof of Theorem an4s

Step	Hyp	Ref	Expression
1		an4 797	. 2 |- (((ph /\ ch) /\ (ps /\ th)) <-> ((ph /\ ps) /\ (ch /\ th)))
2		an4s.1	. 2 |- (((ph /\ ps) /\ (ch /\ th)) -> ta)
3	1, 2	sylbi 187	1 |- (((ph /\ ch) /\ (ps /\ th)) -> ta)

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  an42s  800  anandis  803  anandirs  804  2mo  2282  fnun  5190  f1co  5265  f1oun  5305  f1oco  5309  fntxp  5805  fnpprod  5844  f1opprod  5845  enprmaplem3  6079  sbthlem3  6206  fnfrec  6321