Theorem bnj836 30830

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

Hypotheses

Ref	Expression
bnj836.1	|- ( et <-> ( ph /\ ps /\ ch ) )
bnj836.2	|- ( ps -> ta )

Assertion

Ref	Expression
bnj836	|- ( et -> ta )

Proof of Theorem bnj836

Step	Hyp	Ref	Expression
1		bnj836.1	. 2 |- ( et <-> ( ph /\ ps /\ ch ) )
2		bnj836.2	. . 3 |- ( ps -> ta )
3	2	3ad2ant2 1083	. 2 |- ( ( ph /\ ps /\ ch ) -> ta )
4	1, 3	sylbi 207	1 |- ( et -> ta )

Syntax hints:   -> wi 4   <-> wb 196   /\ w3a 1037

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

This theorem is referenced by:  bnj1379  30901  bnj1175  31072  bnj1286  31087  bnj1450  31118  bnj1501  31135  bnj1523  31139