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Theorem rabbieq 36460
Description: Equivalent wff's correspond to restricted class abstractions which are equal with the same class. (Contributed by Peter Mazsa, 8-Jul-2019.)
Hypotheses
Ref Expression
rabbieq.1 𝐵 = {𝑥𝐴𝜑}
rabbieq.2 (𝜑𝜓)
Assertion
Ref Expression
rabbieq 𝐵 = {𝑥𝐴𝜓}

Proof of Theorem rabbieq
StepHypRef Expression
1 rabbieq.1 . 2 𝐵 = {𝑥𝐴𝜑}
2 rabbieq.2 . . 3 (𝜑𝜓)
32rabbii 3415 . 2 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
41, 3eqtri 2764 1 𝐵 = {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1539  {crab 3303
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-9 2114  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1780  df-sb 2066  df-clab 2714  df-cleq 2728  df-rab 3306
This theorem is referenced by:  dfrefrels3  36728  dfcnvrefrels3  36743  dfsymrels3  36760  refsymrels3  36780  dftrrels3  36790  dfeqvrels3  36803  dfdisjs3  36924  dfdisjs4  36925
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