Theorem bnj253 31372

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 31368	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
2		df-3an 1073	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
3	1, 2	bitr4i 270	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃))

Syntax hints:   ↔ wb 198   ∧ wa 386   ∧ w3a 1071   ∧ w-bnj17 31354

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 199  df-an 387  df-3an 1073  df-bnj17 31355

This theorem is referenced by:  bnj543  31562  bnj558  31571  bnj594  31581  bnj917  31603  bnj929  31605  bnj944  31607  bnj978  31618  bnj998  31625  bnj1006  31628