Theorem simprr2 1077

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

Assertion

Ref	Expression
simprr2	|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )

Proof of Theorem simprr2

Step	Hyp	Ref	Expression
1		simpr2 1035	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantl 277	1 |- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )

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:  icodiamlt  11946  summodc  12150  prodmodc  12345  ivthreinc  15746