Theorem bnj706 32135

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 32130	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜓)
2		bnj706.1	. 2 ⊢ (𝜓 → 𝜏)
3	1, 2	syl 17	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Syntax hints:   → wi 4   ∧ 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:  bnj770  32144  bnj938  32319  bnj964  32325  bnj1001  32341  bnj1006  32342  bnj1110  32364