Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  anim1d GIF version

Theorem anim1d 323
 Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.)
Hypothesis
Ref Expression
anim1d.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
anim1d (𝜑 → ((𝜓𝜃) → (𝜒𝜃)))

Proof of Theorem anim1d
StepHypRef Expression
1 anim1d.1 . 2 (𝜑 → (𝜓𝜒))
2 idd 21 . 2 (𝜑 → (𝜃𝜃))
31, 2anim12d 322 1 (𝜑 → ((𝜓𝜃) → (𝜒𝜃)))
 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:  pm3.45  539  exdistrfor  1697  mopick2  1999  ssrexv  3033  ssdif  3106  ssrin  3190  reupick  3249  disjss1  3779  copsexg  4009  po3nr  4075  coss2  4520  fununi  4995  recexprlemlol  6782  recexprlemupu  6784  icoshft  8959  2ffzeq  9100  qbtwnxr  9214  ico0  9218  r19.2uz  9820
 Copyright terms: Public domain W3C validator