Theorem dne1 26

Description: Double negation elimination, left hand side.

Hypothesis

Ref	Expression
dne1.1	⊦ (~ ~ 𝜑 ⅋ 𝜓)

Assertion

Ref	Expression
dne1	⊦ (𝜑 ⅋ 𝜓)

Proof of Theorem dne1

Step	Hyp	Ref	Expression
1		dne1.1	. . . 4 ⊦ (~ ~ 𝜑 ⅋ 𝜓)
2	1	mdcoi 12	. . 3 ⊦ (𝜓 ⅋ ~ ~ 𝜑)
3	2	dned 24	. 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:  enenebot  28  iac  35  eac1d  37  eac2d  39