Metamath Proof Explorer

Theorem bnj837

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

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

Proof

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