Theorem bnj291 32590

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 32589	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))
2		df-bnj17 32566	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓))
3	1, 2	bitri 274	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜒 ∧ 𝜃) ∧ 𝜓))

Syntax hints:   ↔ wb 205   ∧ wa 395   ∧ w3a 1085   ∧ w-bnj17 32565

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 206  df-an 396  df-3an 1087  df-bnj17 32566

This theorem is referenced by:  bnj643  32629  bnj938  32817  bnj944  32818