Theorem bnj253 35002

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 34998	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
2		df-3an 1101	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ↔ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃))
3	1, 2	bitr4i 280	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃))

Syntax hints:   ↔ wb 208   ∧ wa 399   ∧ w3a 1099   ∧ w-bnj17 34984

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 209  df-an 400  df-3an 1101  df-bnj17 34985

This theorem is referenced by:  bnj543  35190  bnj558  35199  bnj594  35209  bnj917  35231  bnj929  35233  bnj944  35235  bnj978  35246  bnj998  35254  bnj1006  35257