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Theorem rabbia2 3390
 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 3389 . 2 (⊤ → {𝑥𝐴𝜓} = {𝑥𝐵𝜒})
43mptru 1546 1 {𝑥𝐴𝜓} = {𝑥𝐵𝜒}
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∧ wa 400   = wceq 1539  ⊤wtru 1540   ∈ wcel 2112  {crab 3075 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-rab 3080 This theorem is referenced by:  rabeqi  3395  rabswap  3402  f1ossf1o  6879  finsumvtxdg2ssteplem3  27426  clwlknf1oclwwlkn  27958  clwwlknon2x  27977  numclwwlkovh  28247  ballotlem2  31964  smflim  43766  smflim2  43793  smflimsuplem1  43807  smflimsup  43815  sprvalpwn0  44358
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