Metamath Proof Explorer


Theorem bnj255

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

Ref Expression
Assertion bnj255 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑𝜓 ∧ ( 𝜒𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 bnj251 ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒𝜃 ) ) ) )
2 3anass ( ( 𝜑𝜓 ∧ ( 𝜒𝜃 ) ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒𝜃 ) ) ) )
3 1 2 bitr4i ( ( 𝜑𝜓𝜒𝜃 ) ↔ ( 𝜑𝜓 ∧ ( 𝜒𝜃 ) ) )