Theorem pm5.53 1022

Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.53	⊢ ((((𝜑 ∨ 𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑 → 𝜃) ∧ (𝜓 → 𝜃)) ∧ (𝜒 → 𝜃)))

Proof of Theorem pm5.53

Step	Hyp	Ref	Expression
1		jaob 976	. 2 ⊢ ((((𝜑 ∨ 𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑 ∨ 𝜓) → 𝜃) ∧ (𝜒 → 𝜃)))
2		jaob 976	. 2 ⊢ (((𝜑 ∨ 𝜓) → 𝜃) ↔ ((𝜑 → 𝜃) ∧ (𝜓 → 𝜃)))
3	1, 2	bianbi 639	1 ⊢ ((((𝜑 ∨ 𝜓) ∨ 𝜒) → 𝜃) ↔ (((𝜑 → 𝜃) ∧ (𝜓 → 𝜃)) ∧ (𝜒 → 𝜃)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401   ∨ wo 861

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-or 862

This theorem is used by:  3jaob  1453