ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adantl3 GIF version

Theorem 3adantl3 1140
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
3adantl3 (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adantl3
StepHypRef Expression
1 3simpa 979 . 2 ((𝜑𝜓𝜏) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 281 1 (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 963
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 depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  ltsopr  7516  lediv2a  8766  muldvds1  11711  muldvds2  11712  dvdscmul  11713  dvdsmulc  11714  rpexp  12027  iscnp4  12618  cnpnei  12619  xblm  12817
  Copyright terms: Public domain W3C validator