Theorem bnj721 32023

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

Hypothesis

Ref	Expression
bnj721.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)

Assertion

Ref	Expression
bnj721	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Proof of Theorem bnj721

Step	Hyp	Ref	Expression
1		bnj658 32017	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜑 ∧ 𝜓 ∧ 𝜒))
2		bnj721.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
3	1, 2	syl 17	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Syntax hints:   → wi 4   ∧ w3a 1083   ∧ w-bnj17 31951

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 31952

This theorem is referenced by:  bnj570  32172  bnj594  32179  bnj999  32225  bnj1093  32247