Theorem mdco 108

Description: ⅋ is commutative.

Assertion

Ref	Expression
mdco	⊦ ((𝜑 ⅋ 𝜓) ⊸ (𝜓 ⅋ 𝜑))

Proof of Theorem mdco

Step	Hyp	Ref	Expression
1		ax-init 7	. . 3 ⊦ (~ (𝜑 ⅋ 𝜓) ⅋ (𝜑 ⅋ 𝜓))
2	1	mdcod 11	. 2 ⊦ (~ (𝜑 ⅋ 𝜓) ⅋ (𝜓 ⅋ 𝜑))
3	2	dfli2i 66	1 ⊦ ((𝜑 ⅋ 𝜓) ⊸ (𝜓 ⅋ 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:  mdcob  109