Theorem simp2i 1038

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 1029	. 2 |- ( ( ph /\ ps /\ ch ) -> ps )
3	1, 2	ax-mp 5	1 |- ps

This proof depends on syntax axioms:   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  strleun  13458  rmodislmodlem  14687  rmodislmod  14688  sratsetg  14782  sradsg  14785  birthdaylog2  16090  lgslem4  16122  lgscllem  16126  lgsdir2lem2  16148