Theorem bnj706 30078

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 30073	. 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 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:  bnj770  30087  bnj938  30261  bnj964  30267  bnj1001  30282  bnj1006  30283  bnj1110  30304