Linear Logic Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > LLPE Home > Th. List > lbeui | Structured version |
Description: Linear biconditional is Euclidean. Inference for lbeu 126. |
Ref | Expression |
---|---|
lbeui.1 | ⊦ (𝜑 ⧟ 𝜓) |
lbeui.2 | ⊦ (𝜑 ⧟ 𝜒) |
Ref | Expression |
---|---|
lbeui | ⊦ (𝜓 ⧟ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lbeui.1 | . . . 4 ⊦ (𝜑 ⧟ 𝜓) | |
2 | 1 | lbi2 90 | . . 3 ⊦ (𝜓 ⊸ 𝜑) |
3 | lbeui.2 | . . . 4 ⊦ (𝜑 ⧟ 𝜒) | |
4 | 3 | lbi1 89 | . . 3 ⊦ (𝜑 ⊸ 𝜒) |
5 | 2, 4 | syl 75 | . 2 ⊦ (𝜓 ⊸ 𝜒) |
6 | 3 | lbi2 90 | . . 3 ⊦ (𝜒 ⊸ 𝜑) |
7 | 1 | lbi1 89 | . . 3 ⊦ (𝜑 ⊸ 𝜓) |
8 | 6, 7 | syl 75 | . 2 ⊦ (𝜒 ⊸ 𝜓) |
9 | 5, 8 | ilb 96 | 1 ⊦ (𝜓 ⧟ 𝜒) |
Colors of variables: wff var nilad |
Syntax hints: ⧟ 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: lbsymi 100 lbtri 101 |
Copyright terms: Public domain | W3C validator |