ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anim2d GIF version

Theorem anim2d 324
Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
anim1d.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
anim2d (𝜑 → ((𝜃𝜓) → (𝜃𝜒)))

Proof of Theorem anim2d
StepHypRef Expression
1 idd 21 . 2 (𝜑 → (𝜃𝜃))
2 anim1d.1 . 2 (𝜑 → (𝜓𝜒))
31, 2anim12d 322 1 (𝜑 → ((𝜃𝜓) → (𝜃𝜒)))
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:  spsbim  1740  ssel  2966  sscon  3104  uniss  3628  trel3  3889  copsexg  4008  ssopab2  4039  coss1  4518  fununi  4994  imadif  5006  fss  5081  ssimaex  5261  opabbrex  5576  ssoprab2  5588  poxp  5880  xpdom2  6335  qbtwnxr  9213  ioc0  9218  climshftlemg  10053
  Copyright terms: Public domain W3C validator