ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant3r3 GIF version

Theorem 3adant3r3 1177
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r3 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

Proof of Theorem 3adant3r3
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expb 1167 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323adantr3 1127 1 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
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 949
This theorem is referenced by:  mettri2  12458  xmetrtri  12472
  Copyright terms: Public domain W3C validator