Theorem simp1i 996

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 987	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
3	1, 2	ax-mp 5	1 |- ph

Syntax hints:   /\ w3a 968

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 970

This theorem is referenced by:  find  4576  structfn  12413  strleun  12484  lgslem4  13544  lgscllem  13548  lgsdir2lem2  13570