Theorem bnj837 32109

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

Hypotheses

Ref	Expression
bnj837.1	|- ( et <-> ( ph /\ ps /\ ch ) )
bnj837.2	|- ( ch -> ta )

Assertion

Ref	Expression
bnj837	|- ( et -> ta )

Proof of Theorem bnj837

Step	Hyp	Ref	Expression
1		bnj837.1	. 2 |- ( et <-> ( ph /\ ps /\ ch ) )
2		bnj837.2	. . 3 |- ( ch -> ta )
3	2	3ad2ant3 1011	. 2 |- ( ( ph /\ ps /\ ch ) -> ta )
4	1, 3	sylbi 195	1 |- ( et -> ta )

Syntax hints:   -> wi 4   <-> wb 184   /\ w3a 965

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 185  df-an 371  df-3an 967

This theorem is referenced by:  bnj1379  32179  bnj557  32249  bnj1175  32350  bnj1189  32355  bnj1417  32387