Theorem bnj291 32091

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

Assertion

Ref	Expression
bnj291	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓))

Proof of Theorem bnj291

Step	Hyp	Ref	Expression
1		bnj290 32090	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))
2		df-bnj17 32067	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓))
3	1, 2	bitri 278	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓))

Syntax hints:   ↔ wb 209   ∧ wa 399   ∧ w3a 1084   ∧ w-bnj17 32066

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1086  df-bnj17 32067

This theorem is referenced by:  bnj643  32130  bnj938  32319  bnj944  32320