Theorem orassoc-P3.38 322

Description: '∨' Associativity. †

Assertion

Ref	Expression
orassoc-P3.38	⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))

Proof of Theorem orassoc-P3.38

Step	Hyp	Ref	Expression
1		orassoc-P3.38-L1 320	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		orassoc-P3.38-L2 321	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → ((𝜑 ∨ 𝜓) ∨ 𝜒))
3	1, 2	rcp-NDBII0 239	1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))

Syntax hints:   ↔ wff-bi 104   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by:  orassoc2a-P4  572  orassoc2b-P4  574