Metamath Proof Explorer


Theorem bnj256

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

Ref Expression
Assertion bnj256 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 bnj248 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) )
2 anass ( ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ↔ ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) )
3 1 2 bitri ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) )