Theorem ndnegi-P3.3.CL 242

Description: Closed Form of ndnegi-P3.3 168. †

Assertion

Ref	Expression
ndnegi-P3.3.CL	⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓)) → ¬ 𝜑)

Proof of Theorem ndnegi-P3.3.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM3of3 197	. . 3 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓) ∧ 𝜑) → 𝜑)
2		rcp-NDASM1of3 195	. . 3 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓) ∧ 𝜑) → (𝜑 → 𝜓))
3	1, 2	ndime-P3.6 171	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓) ∧ 𝜑) → 𝜓)
4		rcp-NDASM2of3 196	. . 3 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓) ∧ 𝜑) → (𝜑 → ¬ 𝜓))
5	1, 4	ndime-P3.6 171	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓) ∧ 𝜑) → ¬ 𝜓)
6	3, 5	rcp-NDNEGI3 220	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → ¬ 𝜓)) → ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132   ∧ wff-rcp-AND3 160

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-true-D2.4 155  df-rcp-AND3 161

This theorem is referenced by: (None)