Theorem bnj645 35381

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 35318	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃))
2	1	simprbi 503	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ 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-bnj17 35318

This theorem is used by:  bnj708  35387  bnj908  35561  bnj929  35566  bnj964  35573  bnj1110  35612