LLPE Home Linear Logic Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  LLPE Home  >  Th. List  >  acm2s Structured version  

Theorem acm2s 85
Description: With is monotone in its second argument. Syllogism form of acm2 81.
Hypothesis
Ref Expression
acm2s.1 (𝜓𝜒)
Assertion
Ref Expression
acm2s ((𝜑 & 𝜓) ⊸ (𝜑 & 𝜒))

Proof of Theorem acm2s
StepHypRef Expression
1 ax-init 7 . . 3 (~ (𝜑 & 𝜓) ⅋ (𝜑 & 𝜓))
2 acm2s.1 . . 3 (𝜓𝜒)
31, 2acm2 81 . 2 (~ (𝜑 & 𝜓) ⅋ (𝜑 & 𝜒))
43dfli2i 66 1 ((𝜑 & 𝜓) ⊸ (𝜑 & 𝜒))
Colors of variables: wff var nilad
Syntax hints:  ~ wneg 3   & wac 30  wli 61
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:  dflb2s  92
  Copyright terms: Public domain W3C validator