Theorem lb1i 59

Description: Forward inference using ⧟.

Hypotheses

Ref	Expression
lb1i.1	⊦ 𝜑
lb1i.2	⊦ (𝜑 ⧟ 𝜓)

Assertion

Ref	Expression
lb1i	⊦ 𝜓

Proof of Theorem lb1i

Step	Hyp	Ref	Expression
1		lb1i.1	. . . 4 ⊦ 𝜑
2	1	ax-ibot 4	. . 3 ⊦ (⊥ ⅋ 𝜑)
3		lb1i.2	. . 3 ⊦ (𝜑 ⧟ 𝜓)
4	2, 3	lb1d 57	. 2 ⊦ (⊥ ⅋ 𝜓)
5	4	ax-ebot 5	1 ⊦ 𝜓

Syntax hints:  ⊥wbot 1   ⧟ wlb 55

This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-eac1 33

This theorem depends on definitions:  df-lb 56

This theorem is referenced by:  mdm2  69  syl  75