Theorem dnegi-P3.29 273

Description: Double Negation Introduction. †

This statement does not require ndexclmid-P3.16 181, and is thus deducible with intuitionist logic.

Hypothesis

Ref	Expression
dnegi-P3.29.1	⊢ (𝛾 → 𝜑)

Assertion

Ref	Expression
dnegi-P3.29	⊢ (𝛾 → ¬ ¬ 𝜑)

Proof of Theorem dnegi-P3.29

Step	Hyp	Ref	Expression
1		dnegi-P3.29.1	. . 3 ⊢ (𝛾 → 𝜑)
2	1	rcp-NDIMP1add1 208	. 2 ⊢ ((𝛾 ∧ ¬ 𝜑) → 𝜑)
3		rcp-NDASM2of2 194	. 2 ⊢ ((𝛾 ∧ ¬ 𝜑) → ¬ 𝜑)
4	2, 3	rcp-NDNEGI2 219	1 ⊢ (𝛾 → ¬ ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

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

This theorem is referenced by:  dnegi-P3.29.RC  274  dnegi-P3.29.CL  275  dnegeint-P4.12  421