Theorem lb1s 67

Description: Forward syllogism using ⧟.

Hypotheses

Ref	Expression
lb1s.1	⊦ (𝜑 ⊸ 𝜓)
lb1s.2	⊦ (𝜓 ⧟ 𝜒)

Assertion

Ref	Expression
lb1s	⊦ (𝜑 ⊸ 𝜒)

Proof of Theorem lb1s

Step	Hyp	Ref	Expression
1		lb1s.1	. . . 4 ⊦ (𝜑 ⊸ 𝜓)
2	1	dfli1i 65	. . 3 ⊦ (~ 𝜑 ⅋ 𝜓)
3		lb1s.2	. . 3 ⊦ (𝜓 ⧟ 𝜒)
4	2, 3	lb1d 57	. 2 ⊦ (~ 𝜑 ⅋ 𝜒)
5	4	dfli2i 66	1 ⊦ (𝜑 ⊸ 𝜒)

Syntax hints:  ~ wneg 3   ⧟ wlb 55   ⊸ 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:  licon  94  mcco  115