Metamath Proof Explorer


Theorem bnj446

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

Ref Expression
Assertion bnj446 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( 𝜓𝜒𝜃 ) ∧ 𝜑 ) )

Proof

Step Hyp Ref Expression
1 bnj345 ( ( 𝜓𝜒𝜃𝜑 ) ↔ ( 𝜑𝜓𝜒𝜃 ) )
2 df-bnj17 ( ( 𝜓𝜒𝜃𝜑 ) ↔ ( ( 𝜓𝜒𝜃 ) ∧ 𝜑 ) )
3 1 2 bitr3i ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( 𝜓𝜒𝜃 ) ∧ 𝜑 ) )