Theorem bnj446 35348

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 35345	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜑) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
2		df-bnj17 35318	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜑) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))
3	1, 2	bitr3i 280	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 401   ∧ w3a 1103   ∧ w-bnj17 35317

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-bnj17 35318

This theorem is used by:  bnj642  35379  bnj667  35383  bnj594  35542