Theorem bnj252 33714

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 33712	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)))
2		df-3an 1090	. . 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 205   ∧ wa 397   ∧ w3a 1088   ∧ w-bnj17 33697

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 398  df-3an 1090  df-bnj17 33698

This theorem is referenced by:  bnj290  33721  bnj563  33754  bnj919  33778  bnj976  33788  bnj543  33904  bnj570  33916  bnj594  33923  bnj916  33944  bnj917  33945  bnj964  33954  bnj983  33962  bnj984  33963  bnj998  33968  bnj999  33969  bnj1021  33977  bnj1083  33989  bnj1450  34061