Theorem bnj705 35151

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

Hypothesis

Ref	Expression
bnj705.1	⊢ (𝜑 → 𝜏)

Assertion

Ref	Expression
bnj705	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Proof of Theorem bnj705

Step	Hyp	Ref	Expression
1		bnj642 35146	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜑)
2		bnj705.1	. 2 ⊢ (𝜑 → 𝜏)
3	1, 2	syl 18	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ w-bnj17 35084

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 401  df-3an 1104  df-bnj17 35085

This theorem is used by:  bnj769  35160  bnj998  35354  bnj1006  35357