Theorem bnj432 35114

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

Assertion

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

Proof of Theorem bnj432

Step	Hyp	Ref	Expression
1		bnj422 35113	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓))
2		bnj256 35104	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑 ∧ 𝜓) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))
3	1, 2	bitri 278	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜒 ∧ 𝜃) ∧ (𝜑 ∧ 𝜓)))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 400   ∧ w-bnj17 35084

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-3an 1104  df-bnj17 35085

This theorem is used by:  bnj605  35304  bnj600  35316