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Theorem rabbii 2735
Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2738. (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 2734 1 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
Colors of variables: wff set class
Syntax hints:  wb 105   = wceq 1363  wcel 2158  {crab 2469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-rab 2474
This theorem is referenced by:  dfdif3  3257  suplocexpr  7737  dmtopon  13750
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