Theorem dn 107

Description: Double negation elimination and introduction.

Assertion

Ref	Expression
dn	⊦ (𝜑 ⧟ ~ ~ 𝜑)

Proof of Theorem dn

Step	Hyp	Ref	Expression
1		dnis 78	. 2 ⊦ (𝜑 ⊸ ~ ~ 𝜑)
2		dnes 79	. 2 ⊦ (~ ~ 𝜑 ⊸ 𝜑)
3	1, 2	ilb 96	1 ⊦ (𝜑 ⧟ ~ ~ 𝜑)

Syntax hints:  ~ wneg 3   ⧟ wlb 55

This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-iac 32  ax-eac1 33  ax-eac2 34

This theorem depends on definitions:  df-lb 56  df-li 62

This theorem is referenced by: (None)