Theorem bnj769 32143

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 32134	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
4	1, 3	sylbi 220	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 209   ∧ w-bnj17 32066

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-3an 1086  df-bnj17 32067

This theorem is referenced by:  bnj966  32326  bnj967  32327  bnj986  32337  bnj1053  32358  bnj1030  32369  bnj1133  32371  bnj1450  32432