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Metamath Proof Explorer

Theorem bnj432

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

Ref Expression
Assertion bnj432 ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step Hyp Ref Expression
1 bnj422 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓 ) )
2 bnj256 ⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓 ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜑 ∧ 𝜓 ) ) )
3 1 2 bitri ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ ( 𝜑 ∧ 𝜓 ) ) )