Theorem 3simpb 953

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

Ref	Expression
3simpb	|- ((ph /\ ps /\ ch) -> (ph /\ ch))

Proof of Theorem 3simpb

Step	Hyp	Ref	Expression
1		3ancomb 943	. 2 |- ((ph /\ ps /\ ch) <-> (ph /\ ch /\ ps))
2		3simpa 952	. 2 |- ((ph /\ ch /\ ps) -> (ph /\ ch))
3	1, 2	sylbi 187	1 |- ((ph /\ ps /\ ch) -> (ph /\ ch))

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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  df-3an 936

This theorem is referenced by:  3adant2  974  3adantl2  1112  3adantr2  1115