Theorem bnj771 30834

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

Hypotheses

Ref	Expression
bnj771.1	|- ( et <-> ( ph /\ ps /\ ch /\ th ) )
bnj771.2	|- ( ch -> ta )

Assertion

Ref	Expression
bnj771	|- ( et -> ta )

Proof of Theorem bnj771

Step	Hyp	Ref	Expression
1		bnj771.1	. 2 |- ( et <-> ( ph /\ ps /\ ch /\ th ) )
2		bnj771.2	. . 3 |- ( ch -> ta )
3	2	bnj707 30825	. 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:  bnj1247  30879  bnj996  31025  bnj1097  31049  bnj1145  31061  bnj1259  31084  bnj1296  31089  bnj1450  31118