Theorem simp3i 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
simp3i	|- ch

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 |- ( ph /\ ps /\ ch )
2		simp3 999	. 2 |- ( ( ph /\ ps /\ ch ) -> ch )
3	1, 2	ax-mp 5	1 |- ch

Syntax hints:   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 980

This theorem is referenced by:  structfn  12472  strleun  12554  lgslem4  14266  lgscllem  14270  lgsdir2lem2  14292  lgsdir2lem3  14293