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Theorem rabbieq 35393
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 3471 . 2 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
41, 3eqtri 2841 1 𝐵 = {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wb 207   = wceq 1528  {crab 3139
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-9 2115  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-rab 3144
This theorem is referenced by:  dfrefrels3  35634  dfcnvrefrels3  35647  dfsymrels3  35662  refsymrels3  35682  dftrrels3  35692  dfeqvrels3  35704  dfdisjs3  35823  dfdisjs4  35824
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