Theorem bnj312 30031

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

Assertion

Ref	Expression
bnj312	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒 ∧ 𝜃))

Proof of Theorem bnj312

Step	Hyp	Ref	Expression
1		3ancoma 1038	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
2	1	anbi1i 727	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ↔ ((𝜓 ∧ 𝜑 ∧ 𝜒) ∧ 𝜃))
3		df-bnj17 30006	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃))
4		df-bnj17 30006	. 2 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜑 ∧ 𝜒) ∧ 𝜃))
5	2, 3, 4	3bitr4i 291	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒 ∧ 𝜃))

Syntax hints:   ↔ wb 195   ∧ wa 383   ∧ w3a 1031   ∧ w-bnj17 30005

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 196  df-an 385  df-3an 1033  df-bnj17 30006

This theorem is referenced by:  bnj334  30032  bnj563  30067  bnj953  30263