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Theorem rabbia2 3369
Description: Equivalent wff's yield equal restricted class abstractions. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
rabbia2.1 ((𝑥𝐴𝜓) ↔ (𝑥𝐵𝜒))
Assertion
Ref Expression
rabbia2 {𝑥𝐴𝜓} = {𝑥𝐵𝜒}

Proof of Theorem rabbia2
StepHypRef Expression
1 rabbia2.1 . . . 4 ((𝑥𝐴𝜓) ↔ (𝑥𝐵𝜒))
21a1i 11 . . 3 (⊤ → ((𝑥𝐴𝜓) ↔ (𝑥𝐵𝜒)))
32rabbidva2 3368 . 2 (⊤ → {𝑥𝐴𝜓} = {𝑥𝐵𝜒})
43mptru 1661 1 {𝑥𝐴𝜓} = {𝑥𝐵𝜒}
Colors of variables: wff setvar class
Syntax hints:  wb 198  wa 385   = wceq 1653  wtru 1654  wcel 2157  {crab 3091
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2775
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2784  df-cleq 2790  df-clel 2793  df-rab 3096
This theorem is referenced by:  f1ossf1o  6620  finsumvtxdg2ssteplem3  26788  clwlknf1oclwwlkn  27407  clwlknf1oclwwlknOLD  27409  clwwlknon2x  27433  numclwwlkovh  27737  smflim  41718  smflim2  41745  smflimsuplem1  41759  smflimsup  41767  sprvalpwn0  42519
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