Theorem bnj770 30087

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 30078	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
4	1, 3	sylbi 206	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 195   ∧ w-bnj17 30005

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 196  df-an 385  df-3an 1033  df-bnj17 30006

This theorem is referenced by:  bnj1235  30129  bnj605  30231  bnj607  30240  bnj983  30275  bnj1110  30304  bnj1145  30315  bnj1256  30337  bnj1296  30343  bnj1450  30372