Theorem bnj642 35001

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 34970	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑))
2	1	simprbi 500	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1095   ∧ w-bnj17 34939

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-3an 1097  df-bnj17 34940

This theorem is referenced by:  bnj705  35006  bnj1232  35055  bnj908  35183  bnj1110  35234