Theorem orcomm-P3.37-L1 318

Description: Lemma for orcomm-P3.37 319. †

Assertion

Ref	Expression
orcomm-P3.37-L1	⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Proof of Theorem orcomm-P3.37-L1

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ (((𝜑 ∨ 𝜓) ∧ 𝜑) → 𝜑)
2	1	ndoril-P3.10 175	. 2 ⊢ (((𝜑 ∨ 𝜓) ∧ 𝜑) → (𝜓 ∨ 𝜑))
3		rcp-NDASM2of2 194	. . 3 ⊢ (((𝜑 ∨ 𝜓) ∧ 𝜓) → 𝜓)
4	3	ndorir-P3.11 176	. 2 ⊢ (((𝜑 ∨ 𝜓) ∧ 𝜓) → (𝜓 ∨ 𝜑))
5		rcp-NDASM1of1 192	. 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜓))
6	2, 4, 5	rcp-NDORE2 235	1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑))

Syntax hints:   → wff-imp 10   ∧ wff-and 132   ∨ 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

This theorem is referenced by:  orcomm-P3.37  319