Theorem mdcob 109

Description: ⅋ is commutative. Biconditional version of mdco 108.

Assertion

Ref	Expression
mdcob	⊦ ((𝜑 ⅋ 𝜓) ⧟ (𝜓 ⅋ 𝜑))

Proof of Theorem mdcob

Step	Hyp	Ref	Expression
1		mdco 108	. 2 ⊦ ((𝜑 ⅋ 𝜓) ⊸ (𝜓 ⅋ 𝜑))
2		mdco 108	. 2 ⊦ ((𝜓 ⅋ 𝜑) ⊸ (𝜑 ⅋ 𝜓))
3	1, 2	ilb 96	1 ⊦ ((𝜑 ⅋ 𝜓) ⧟ (𝜓 ⅋ 𝜑))

Syntax hints:   ⅋ wmd 2   ⧟ 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:  md2  114