Theorem dnis 78

Description: Double negation introduction. Syllogism form of dnid 23.

Assertion

Ref	Expression
dnis	⊦ (𝜑 ⊸ ~ ~ 𝜑)

Proof of Theorem dnis

Step	Hyp	Ref	Expression
1		ax-init 7	. . 3 ⊦ (~ ~ 𝜑 ⅋ ~ 𝜑)
2	1	mdcoi 12	. 2 ⊦ (~ 𝜑 ⅋ ~ ~ 𝜑)
3		df-li 62	. 2 ⊦ ((𝜑 ⊸ ~ ~ 𝜑) ⧟ (~ 𝜑 ⅋ ~ ~ 𝜑))
4	2, 3	lb2i 60	1 ⊦ (𝜑 ⊸ ~ ~ 𝜑)

Syntax hints:   ⅋ wmd 2  ~ wneg 3   ⊸ wli 61

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

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

This theorem is referenced by:  licon  94  dn  107  mcco  115