Theorem orasim-P3.48-L2 360

Description: Lemma for orasim-P3.48a 361.

Assertion

Ref	Expression
orasim-P3.48-L2	⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓))

Proof of Theorem orasim-P3.48-L2

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ (((¬ 𝜑 → 𝜓) ∧ 𝜑) → 𝜑)
2	1	ndorir-P3.11 176	. 2 ⊢ (((¬ 𝜑 → 𝜓) ∧ 𝜑) → (𝜑 ∨ 𝜓))
3		rcp-NDASM2of2 194	. . . 4 ⊢ (((¬ 𝜑 → 𝜓) ∧ ¬ 𝜑) → ¬ 𝜑)
4		rcp-NDASM1of2 193	. . . 4 ⊢ (((¬ 𝜑 → 𝜓) ∧ ¬ 𝜑) → (¬ 𝜑 → 𝜓))
5	3, 4	ndime-P3.6 171	. . 3 ⊢ (((¬ 𝜑 → 𝜓) ∧ ¬ 𝜑) → 𝜓)
6	5	ndoril-P3.10 175	. 2 ⊢ (((¬ 𝜑 → 𝜓) ∧ ¬ 𝜑) → (𝜑 ∨ 𝜓))
7		ndexclmid-P3.16.AC 251	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ ¬ 𝜑))
8	2, 6, 7	rcp-NDORE2 235	1 ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wff-neg 9   → 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:  orasim-P3.48a  361