Theorem simpll1 977

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpll1	|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ph )

Proof of Theorem simpll1

Step	Hyp	Ref	Expression
1		simpl1 941	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ph )
2	1	adantr 270	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  fidifsnen  6355  ordiso2  6446  addlocpr  6726  expival  9478  dvdslegcd  10356  lcmledvds  10452  divgcdcoprm0  10483  rpexp  10532