Theorem bnj251 31972

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

Assertion

Ref	Expression
bnj251	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))

Proof of Theorem bnj251

Step	Hyp	Ref	Expression
1		bnj250 31971	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)))
2		anass 471	. . 3 ⊢ (((𝜓 ∧ 𝜒) ∧ 𝜃) ↔ (𝜓 ∧ (𝜒 ∧ 𝜃)))
3	2	anbi2i 624	. 2 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))
4	1, 3	bitri 277	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))

Syntax hints:   ↔ wb 208   ∧ wa 398   ∧ w-bnj17 31956

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 1085  df-bnj17 31957

This theorem is referenced by:  bnj255  31975  bnj535  32162  bnj570  32177  bnj953  32211  bnj1110  32254