Theorem simp1i 1037

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 1028	. 2 |- ( ( ph /\ ps /\ ch ) -> ph )
3	1, 2	ax-mp 5	1 |- ph

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

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

This theorem is used by:  find  4748  structfn  13429  strleun  13517  rmodislmodlem  14796  rmodislmod  14797  sratsetg  14891  sradsg  14894  lgslem4  16327  lgscllem  16331  lgsdir2lem2  16353