Theorem bnj645 30820

Description: /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj645	|- ( ( ph /\ ps /\ ch /\ th ) -> th )

Proof of Theorem bnj645

Step	Hyp	Ref	Expression
1		df-bnj17 30753	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )
2	1	simprbi 480	1 |- ( ( ph /\ ps /\ ch /\ th ) -> th )

Syntax hints:   -> wi 4   /\ w3a 1037   /\ w-bnj17 30752

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-bnj17 30753

This theorem is referenced by:  bnj708  30826  bnj908  31001  bnj929  31006  bnj964  31013  bnj1110  31050