Theorem bnj645 32300

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

Assertion

Ref	Expression
bnj645	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃)

Proof of Theorem bnj645

Step	Hyp	Ref	Expression
1		df-bnj17 32236	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃))
2	1	simprbi 500	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1088   ∧ w-bnj17 32235

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 210  df-an 400  df-bnj17 32236

This theorem is referenced by:  bnj708  32306  bnj908  32482  bnj929  32487  bnj964  32494  bnj1110  32533