Theorem bnj253 33646

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 33642	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
2		df-3an 1090	. 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 205   ∧ wa 397   ∧ w3a 1088   ∧ w-bnj17 33628

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 33629

This theorem is referenced by:  bnj543  33835  bnj558  33844  bnj594  33854  bnj917  33876  bnj929  33878  bnj944  33880  bnj978  33891  bnj998  33899  bnj1006  33902