Theorem simp2i 1009

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	|- ( ph /\ ps /\ ch )

Assertion

Ref	Expression
simp2i	|- ps

Proof of Theorem simp2i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 |- ( ph /\ ps /\ ch )
2		simp2 1000	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
3	1, 2	ax-mp 5	1 |- ps

Syntax hints:   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  strleun  12807  rmodislmodlem  13982  rmodislmod  13983  sratsetg  14077  sradsg  14080  lgslem4  15328  lgscllem  15332  lgsdir2lem2  15354