Metamath Proof Explorer


Theorem bnj258

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

Ref Expression
Assertion bnj258 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( 𝜑𝜓𝜃 ) ∧ 𝜒 ) )

Proof

Step Hyp Ref Expression
1 bnj257 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑𝜓𝜃𝜒 ) )
2 df-bnj17 ( ( 𝜑𝜓𝜃𝜒 ) ↔ ( ( 𝜑𝜓𝜃 ) ∧ 𝜒 ) )
3 1 2 bitri ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( 𝜑𝜓𝜃 ) ∧ 𝜒 ) )