Theorem bnj642 35314

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

Assertion

Ref	Expression
bnj642	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜑)

Proof of Theorem bnj642

Step	Hyp	Ref	Expression
1		bnj446 35283	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))
2	1	simprbi 503	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103   ∧ w-bnj17 35252

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 35253

This theorem is used by:  bnj705  35319  bnj1232  35368  bnj908  35496  bnj1110  35547