Metamath Proof Explorer


Theorem bnj835

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

Ref Expression
Hypotheses bnj835.1 ( 𝜂 ↔ ( 𝜑𝜓𝜒 ) )
bnj835.2 ( 𝜑𝜏 )
Assertion bnj835 ( 𝜂𝜏 )

Proof

Step Hyp Ref Expression
1 bnj835.1 ( 𝜂 ↔ ( 𝜑𝜓𝜒 ) )
2 bnj835.2 ( 𝜑𝜏 )
3 2 3ad2ant1 ( ( 𝜑𝜓𝜒 ) → 𝜏 )
4 1 3 sylbi ( 𝜂𝜏 )