Theorem bnj769 30832

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

Hypotheses

Ref	Expression
bnj769.1	|- ( et <-> ( ph /\ ps /\ ch /\ th ) )
bnj769.2	|- ( ph -> ta )

Assertion

Ref	Expression
bnj769	|- ( et -> ta )

Proof of Theorem bnj769

Step	Hyp	Ref	Expression
1		bnj769.1	. 2 |- ( et <-> ( ph /\ ps /\ ch /\ th ) )
2		bnj769.2	. . 3 |- ( ph -> ta )
3	2	bnj705 30823	. 2 |- ( ( ph /\ ps /\ ch /\ th ) -> ta )
4	1, 3	sylbi 207	1 |- ( et -> ta )

Syntax hints:   -> wi 4   <-> wb 196   /\ 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-3an 1039  df-bnj17 30753

This theorem is referenced by:  bnj966  31014  bnj967  31015  bnj986  31024  bnj1053  31044  bnj1030  31055  bnj1133  31057  bnj1450  31118