Theorem bnj721 35388

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 35382	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜑 ∧ 𝜓 ∧ 𝜒))
2		bnj721.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏)
3	1, 2	syl 18	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103   ∧ w-bnj17 35317

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 35318

This theorem is used by:  bnj570  35535  bnj594  35542  bnj999  35588  bnj1093  35610