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

Theorem rabbii 2601
Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2604. (Contributed by Peter Mazsa, 1-Nov-2019.)
Hypothesis
Ref Expression
rabbii.1 (𝜑𝜓)
Assertion
Ref Expression
rabbii {𝑥𝐴𝜑} = {𝑥𝐴𝜓}

Proof of Theorem rabbii
StepHypRef Expression
1 rabbii.1 . . 3 (𝜑𝜓)
21a1i 9 . 2 (𝑥𝐴 → (𝜑𝜓))
32rabbiia 2600 1 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1287  wcel 1436  {crab 2359
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-rab 2364
This theorem is referenced by:  dfdif3  3099
  Copyright terms: Public domain W3C validator