Theorem md2 114

Description: ⊥ is the unit of ⅋ (right side).

Assertion

Ref	Expression
md2	⊦ (𝜑 ⧟ (𝜑 ⅋ ⊥))

Proof of Theorem md2

Step	Hyp	Ref	Expression
1		md1 113	. . . 4 ⊦ (𝜑 ⧟ (⊥ ⅋ 𝜑))
2	1	lbi1 89	. . 3 ⊦ (𝜑 ⊸ (⊥ ⅋ 𝜑))
3		mdcob 109	. . . 4 ⊦ ((𝜑 ⅋ ⊥) ⧟ (⊥ ⅋ 𝜑))
4	3	lbi2 90	. . 3 ⊦ ((⊥ ⅋ 𝜑) ⊸ (𝜑 ⅋ ⊥))
5	2, 4	syl 75	. 2 ⊦ (𝜑 ⊸ (𝜑 ⅋ ⊥))
6	3	lbi1 89	. . 3 ⊦ ((𝜑 ⅋ ⊥) ⊸ (⊥ ⅋ 𝜑))
7	6, 1	lb2s 68	. 2 ⊦ ((𝜑 ⅋ ⊥) ⊸ 𝜑)
8	5, 7	ilb 96	1 ⊦ (𝜑 ⧟ (𝜑 ⅋ ⊥))

Syntax hints:  ⊥wbot 1   ⅋ 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: (None)