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Theorem rabbieq 35630
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 3448 . 2 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
41, 3eqtri 2845 1 𝐵 = {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wb 209   = wceq 1538  {crab 3134
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-rab 3139
This theorem is referenced by:  dfrefrels3  35872  dfcnvrefrels3  35885  dfsymrels3  35900  refsymrels3  35920  dftrrels3  35930  dfeqvrels3  35942  dfdisjs3  36061  dfdisjs4  36062
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