Theorem bnj770 34777

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

Hypotheses

Ref	Expression
bnj770.1	⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
bnj770.2	⊢ (𝜓 → 𝜏)

Assertion

Ref	Expression
bnj770	⊢ (𝜂 → 𝜏)

Proof of Theorem bnj770

Step	Hyp	Ref	Expression
1		bnj770.1	. 2 ⊢ (𝜂 ↔ (𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃))
2		bnj770.2	. . 3 ⊢ (𝜓 → 𝜏)
3	2	bnj706 34768	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
4	1, 3	sylbi 217	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 206   ∧ w-bnj17 34700

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 207  df-an 396  df-3an 1089  df-bnj17 34701

This theorem is referenced by:  bnj1235  34818  bnj605  34921  bnj607  34930  bnj983  34965  bnj1110  34996  bnj1145  35007  bnj1256  35029  bnj1296  35035  bnj1450  35064