Theorem bnj771 35462

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

Hypotheses

Ref	Expression
bnj771.1	⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
bnj771.2	⊢ (𝜒 → 𝜏)

Assertion

Ref	Expression
bnj771	⊢ (𝜂 → 𝜏)

Proof of Theorem bnj771

Step	Hyp	Ref	Expression
1		bnj771.1	. 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
2		bnj771.2	. . 3 ⊢ (𝜒 → 𝜏)
3	2	bnj707 35453	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
4	1, 3	sylbi 220	1 ⊢ (𝜂 → 𝜏)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ w-bnj17 35384

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 35385

This theorem is used by:  bnj1247  35505  bnj996  35653  bnj1097  35678  bnj1145  35690  bnj1259  35713  bnj1296  35718  bnj1450  35747