Theorem simp1i 1001

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
simp1i	|- ph

Proof of Theorem simp1i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 |- ( ph /\ ps /\ ch )
2		simp1 992	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
3	1, 2	ax-mp 5	1 |- ph

Syntax hints:   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  find  4583  structfn  12435  strleun  12507  lgslem4  13698  lgscllem  13702  lgsdir2lem2  13724