Theorem simp1i 1008

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 999	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
3	1, 2	ax-mp 5	1 |- ph

Syntax hints:   /\ w3a 980

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

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

This theorem is referenced by:  find  4632  structfn  12640  strleun  12725  rmodislmodlem  13849  rmodislmod  13850  sratsetg  13944  sradsg  13947  lgslem4  15160  lgscllem  15164  lgsdir2lem2  15186