Theorem bnj334 34010

Description: ∧-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj334	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))

Proof of Theorem bnj334

Step	Hyp	Ref	Expression
1		bnj290 34007	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))
2		bnj257 34004	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ (𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃))
3		bnj312 34009	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))
4	1, 2, 3	3bitri 296	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))

Syntax hints:   ↔ wb 205   ∧ w-bnj17 33983

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 397  df-3an 1089  df-bnj17 33984

This theorem is referenced by:  bnj345  34011  bnj518  34183  bnj916  34230  bnj929  34233