ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  adantrrr GIF version

Theorem adantrrr 478
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantr2.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
adantrrr ((𝜑 ∧ (𝜓 ∧ (𝜒𝜏))) → 𝜃)

Proof of Theorem adantrrr
StepHypRef Expression
1 simpl 108 . 2 ((𝜒𝜏) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 402 1 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜏))) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  2ndconst  6119  genpdisj  7338  ltexprlemdisj  7421  addsrmo  7558  mulsrmo  7559  axpre-suploclemres  7716  lemul12b  8626  tgcl  12243  neissex  12344
  Copyright terms: Public domain W3C validator