Theorem bnj708 32027

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 32021	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃)
2		bnj708.1	. 2 ⊢ (𝜃 → 𝜏)
3	1, 2	syl 17	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Syntax hints:   → wi 4   ∧ w-bnj17 31956

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 209  df-an 399  df-bnj17 31957

This theorem is referenced by:  bnj1254  32081  bnj999  32230  bnj1001  32231  bnj1006  32232  bnj1049  32246  bnj1121  32257  bnj1145  32265  bnj1154  32271