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Theorem rabbia2 3435
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 3434 . 2 (⊤ → {𝑥𝐴𝜓} = {𝑥𝐵𝜒})
43mptru 1543 1 {𝑥𝐴𝜓} = {𝑥𝐵𝜒}
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395   = wceq 1536  wtru 1537  wcel 2105  {crab 3432
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-rab 3433
This theorem is referenced by:  rabbiia  3436  rabswap  3442  rabeqi  3446  rabrabi  3452  f1ossf1o  7147  finsumvtxdg2ssteplem3  29579  clwlknf1oclwwlkn  30112  clwwlknon2x  30131  numclwwlkovh  30401  ballotlem2  34469  smflim  46732  smflim2  46761  smflimsuplem1  46775  smflimsup  46783  sprvalpwn0  47407
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