Theorem bnj769 35393

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

Hypotheses

Ref	Expression
bnj769.1	⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
bnj769.2	⊢ (𝜑 → 𝜏)

Assertion

Ref	Expression
bnj769	⊢ (𝜂 → 𝜏)

Proof of Theorem bnj769

Step	Hyp	Ref	Expression
1		bnj769.1	. 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
2		bnj769.2	. . 3 ⊢ (𝜑 → 𝜏)
3	2	bnj705 35384	. 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 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:  bnj966  35574  bnj967  35575  bnj986  35585  bnj1053  35606  bnj1030  35617  bnj1133  35619  bnj1450  35680