Theorem bnj706 35385

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

Hypothesis

Ref	Expression
bnj706.1	⊢ (𝜓 → 𝜏)

Assertion

Ref	Expression
bnj706	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Proof of Theorem bnj706

Step	Hyp	Ref	Expression
1		bnj643 35380	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜓)
2		bnj706.1	. 2 ⊢ (𝜓 → 𝜏)
3	1, 2	syl 18	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ 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:  bnj770  35394  bnj938  35567  bnj964  35573  bnj1001  35589  bnj1006  35590  bnj1110  35612