ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adantl2 GIF version

Theorem 3adantl2 1154
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
3adantl2 (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adantl2
StepHypRef Expression
1 3simpb 995 . 2 ((𝜑𝜏𝜓) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 283 1 (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  3ad2antl1  1159  nnmord  6511  ltaprg  7596  lediv2a  8828  zdiv  9317  mulgnn0subcl  12872  mulgsubcl  12873  neiint  13278  cnpnei  13352
  Copyright terms: Public domain W3C validator