Theorem bnj708 35266

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

Hypothesis

Ref	Expression
bnj708.1	⊢ (𝜃 → 𝜏)

Assertion

Ref	Expression
bnj708	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Proof of Theorem bnj708

Step	Hyp	Ref	Expression
1		bnj645 35260	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃)
2		bnj708.1	. 2 ⊢ (𝜃 → 𝜏)
3	1, 2	syl 18	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ w-bnj17 35196

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-bnj17 35197

This theorem is used by:  bnj1254  35318  bnj999  35467  bnj1001  35468  bnj1006  35469  bnj1049  35483  bnj1121  35494  bnj1145  35502  bnj1154  35508