LLPE Home Linear Logic Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  LLPE Home  >  Th. List  >  lbeui Structured version  

Theorem lbeui 99
Description: Linear biconditional is Euclidean. Inference for lbeu 126.
Hypotheses
Ref Expression
lbeui.1 (𝜑𝜓)
lbeui.2 (𝜑𝜒)
Assertion
Ref Expression
lbeui (𝜓𝜒)

Proof of Theorem lbeui
StepHypRef Expression
1 lbeui.1 . . . 4 (𝜑𝜓)
21lbi2 90 . . 3 (𝜓𝜑)
3 lbeui.2 . . . 4 (𝜑𝜒)
43lbi1 89 . . 3 (𝜑𝜒)
52, 4syl 75 . 2 (𝜓𝜒)
63lbi2 90 . . 3 (𝜒𝜑)
71lbi1 89 . . 3 (𝜑𝜓)
86, 7syl 75 . 2 (𝜒𝜓)
95, 8ilb 96 1 (𝜓𝜒)
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