Theorem bnj719 12657

Description: /\-manipulation.

Hypothesis

Ref	Expression
bnj719.1	|- ((th /\ ps) -> ta)

Assertion

Ref	Expression
bnj719	|- ((ph /\ ps /\ ch /\ th) -> ta)

Proof of Theorem bnj719

Step	Hyp	Ref	Expression
1		bnj656 12591	. 2 |- ((ph /\ ps /\ ch /\ th) -> (th /\ ps))
2		bnj719.1	. 2 |- ((th /\ ps) -> ta)
3	1, 2	syl 12	1 |- ((ph /\ ps /\ ch /\ th) -> ta)

Syntax hints:   -> wi 3   /\ wa 240   /\ syn-bnj17 12019

This theorem is referenced by:  bnj783 12737

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-3an 860  df-bnj17 12020

Copyright terms: Public domain