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

Theorem anandirs 535
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)
Hypothesis
Ref Expression
anandirs.1 (((𝜑𝜒) ∧ (𝜓𝜒)) → 𝜏)
Assertion
Ref Expression
anandirs (((𝜑𝜓) ∧ 𝜒) → 𝜏)

Proof of Theorem anandirs
StepHypRef Expression
1 anandirs.1 . . 3 (((𝜑𝜒) ∧ (𝜓𝜒)) → 𝜏)
21an4s 530 . 2 (((𝜑𝜓) ∧ (𝜒𝜒)) → 𝜏)
32anabsan2 526 1 (((𝜑𝜓) ∧ 𝜒) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  3impdir  1202  fvreseq  5298  phplem4  6348  muladd  7452  iccshftr  8962  iccshftl  8964  iccdil  8966  icccntr  8968  fzaddel  9023  fzsubel  9024  mulexp  9458
  Copyright terms: Public domain W3C validator