Theorem bnj770 35122

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 35113	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)
4	1, 3	sylbi 220	1 ⊢ (𝜂 → 𝜏)

Syntax hints:   → wi 4   ↔ wb 209   ∧ w-bnj17 35045

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 401  df-3an 1103  df-bnj17 35046

This theorem is referenced by:  bnj1235  35162  bnj605  35265  bnj607  35274  bnj983  35309  bnj1110  35340  bnj1145  35351  bnj1256  35373  bnj1296  35379  bnj1450  35408