Theorem simpl23 1108

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

Assertion

Ref	Expression
simpl23	|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ch )

Proof of Theorem simpl23

Step	Hyp	Ref	Expression
1		simp23 1063	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

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

This theorem is used by:  mulgdirlem  13956