Theorem bnj252 34866

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

Assertion

Ref	Expression
bnj252	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)))

Proof of Theorem bnj252

Step	Hyp	Ref	Expression
1		bnj250 34864	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)))
2		df-3an 1089	. . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜃))
3	2	anbi2i 624	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)))
4	1, 3	bitr4i 278	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)))

Syntax hints:   ↔ wb 206   ∧ wa 395   ∧ w3a 1087   ∧ w-bnj17 34849

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 207  df-an 396  df-3an 1089  df-bnj17 34850

This theorem is referenced by:  bnj290  34873  bnj563  34906  bnj919  34930  bnj976  34940  bnj543  35055  bnj570  35067  bnj594  35074  bnj916  35095  bnj917  35096  bnj964  35105  bnj983  35113  bnj984  35114  bnj998  35119  bnj999  35120  bnj1021  35128  bnj1083  35140  bnj1450  35212