Theorem anabsan 581

Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.) (Revised by NM, 18-Nov-2013.)

Hypothesis

Ref	Expression
anabsan.1	|- ( ( ( ph /\ ph ) /\ ps ) -> ch )

Assertion

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

Proof of Theorem anabsan

Step	Hyp	Ref	Expression
1		pm4.24 399	. 2 |- ( ph <-> ( ph /\ ph ) )
2		anabsan.1	. 2 |- ( ( ( ph /\ ph ) /\ ps ) -> ch )
3	1, 2	sylanb 284	1 |- ( ( ph /\ ps ) -> ch )

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 proof depends on definitions:  df-bi 117

This theorem is used by:  anabss1  582  anabss5  584  anandis  600  iddvds  12571  1dvds  12572