Theorem bnj334 35111

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 35108	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓))
2		bnj257 35105	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓) ↔ (𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃))
3		bnj312 35110	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))
4	1, 2, 3	3bitri 300	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃))

This proof depends on syntax axioms:   ↔ wb 209   ∧ 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:  bnj345  35112  bnj518  35283  bnj916  35330  bnj929  35333