Theorem imasor-P4.32-L1 485

Description: Lemma for imasor-P4.32a 487.

Assertion

Ref	Expression
imasor-P4.32-L1	⊢ ((𝜑 → 𝜓) → (¬ 𝜑 ∨ 𝜓))

Proof of Theorem imasor-P4.32-L1

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . . 4 ⊢ (((𝜑 → 𝜓) ∧ 𝜑) → 𝜑)
2		rcp-NDASM1of2 193	. . . 4 ⊢ (((𝜑 → 𝜓) ∧ 𝜑) → (𝜑 → 𝜓))
3	1, 2	ndime-P3.6 171	. . 3 ⊢ (((𝜑 → 𝜓) ∧ 𝜑) → 𝜓)
4	3	ndoril-P3.10 175	. 2 ⊢ (((𝜑 → 𝜓) ∧ 𝜑) → (¬ 𝜑 ∨ 𝜓))
5		rcp-NDASM2of2 194	. . 3 ⊢ (((𝜑 → 𝜓) ∧ ¬ 𝜑) → ¬ 𝜑)
6	5	ndorir-P3.11 176	. 2 ⊢ (((𝜑 → 𝜓) ∧ ¬ 𝜑) → (¬ 𝜑 ∨ 𝜓))
7		ndexclmid-P3.16.AC 251	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 ∨ ¬ 𝜑))
8	4, 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:  imasor-P4.32a  487