Theorem dni1 25

Description: Double negation introduction, left hand side.

Hypothesis

Ref	Expression
dni1.1	⊦ (𝜑 ⅋ 𝜓)

Assertion

Ref	Expression
dni1	⊦ (~ ~ 𝜑 ⅋ 𝜓)

Proof of Theorem dni1

Step	Hyp	Ref	Expression
1		dni1.1	. . . 4 ⊦ (𝜑 ⅋ 𝜓)
2	1	mdcoi 12	. . 3 ⊦ (𝜓 ⅋ 𝜑)
3	2	dnid 23	. 2 ⊦ (𝜓 ⅋ ~ ~ 𝜑)
4	3	mdcoi 12	1 ⊦ (~ ~ 𝜑 ⅋ 𝜓)

Syntax hints:   ⅋ wmd 2  ~ wneg 3

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

This theorem is referenced by:  inenebot  27  iac  35  eac1d  37  eac2d  39