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

Theorem rabbii 2644
 Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2647. (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 2643 1 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   = wceq 1314   ∈ wcel 1463  {crab 2395 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-rab 2400 This theorem is referenced by:  dfdif3  3154  suplocexpr  7497  dmtopon  12096
 Copyright terms: Public domain W3C validator