Theorem bnj251 32681

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 32680	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)))
2		anass 469	. . 3 ⊢ (((𝜓 ∧ 𝜒) ∧ 𝜃) ↔ (𝜓 ∧ (𝜒 ∧ 𝜃)))
3	2	anbi2i 623	. 2 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))
4	1, 3	bitri 274	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃) ↔ (𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))))

Syntax hints:   ↔ wb 205   ∧ wa 396   ∧ w-bnj17 32665

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 206  df-an 397  df-3an 1088  df-bnj17 32666

This theorem is referenced by:  bnj255  32684  bnj535  32870  bnj570  32885  bnj953  32919  bnj1110  32962