Theorem bnj446 31991

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

Assertion

Ref	Expression
bnj446	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))

Proof of Theorem bnj446

Step	Hyp	Ref	Expression
1		bnj345 31988	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜑) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
2		df-bnj17 31961	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜑) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))
3	1, 2	bitr3i 279	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))

Syntax hints:   ↔ wb 208   ∧ wa 398   ∧ w3a 1083   ∧ w-bnj17 31960

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 399  df-3an 1085  df-bnj17 31961

This theorem is referenced by:  bnj642  32023  bnj667  32027  bnj594  32188