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

Theorem dismdac 46
Description: distributes over &.
Hypothesis
Ref Expression
dismdac.1 (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃)))
Assertion
Ref Expression
dismdac (𝜑 ⅋ ((𝜓𝜒) & (𝜓𝜃)))

Proof of Theorem dismdac
StepHypRef Expression
1 dismdac.1 . . . . 5 (𝜑 ⅋ (𝜓 ⅋ (𝜒 & 𝜃)))
21mdasri 17 . . . 4 ((𝜑𝜓) ⅋ (𝜒 & 𝜃))
32eac1d 37 . . 3 ((𝜑𝜓) ⅋ 𝜒)
43mdasi 14 . 2 (𝜑 ⅋ (𝜓𝜒))
52eac2d 39 . . 3 ((𝜑𝜓) ⅋ 𝜃)
65mdasi 14 . 2 (𝜑 ⅋ (𝜓𝜃))
74, 6iac 35 1 (𝜑 ⅋ ((𝜓𝜒) & (𝜓𝜃)))
Colors of variables: wff var nilad
Syntax hints:  wmd 2   & wac 30
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 is referenced by: (None)
  Copyright terms: Public domain W3C validator