Theorem bnj707 35386

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

Hypothesis

Ref	Expression
bnj707.1	⊢ (𝜒 → 𝜏)

Assertion

Ref	Expression
bnj707	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏)

Proof of Theorem bnj707

Step	Hyp	Ref	Expression
1		bnj258 35339	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒))
2	1	simprbi 503	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜒)
3		bnj707.1	. 2 ⊢ (𝜒 → 𝜏)
4	2, 3	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-3an 1105  df-bnj17 35318

This theorem is used by:  bnj771  35395  bnj998  35587  bnj1001  35589  bnj1006  35590  bnj1053  35606  bnj1121  35615  bnj1030  35617