Theorem bnj253 34867

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

Assertion

Ref	Expression
bnj253	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃))

Proof of Theorem bnj253

Step	Hyp	Ref	Expression
1		bnj248 34863	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
2		df-3an 1089	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
3	1, 2	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:  bnj543  35055  bnj558  35064  bnj594  35074  bnj917  35096  bnj929  35098  bnj944  35100  bnj978  35111  bnj998  35119  bnj1006  35122