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Theorem rabbieq 3442
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 3439 . 2 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
41, 3eqtri 2763 1 𝐵 = {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1537  {crab 3433
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-rab 3434
This theorem is referenced by:  dfdif3  4127  1arithufd  33556  dfrefrels3  38496  dfcnvrefrels3  38511  dfsymrels3  38528  refsymrels3  38548  dftrrels3  38558  dfeqvrels3  38571  dfdisjs3  38692  dfdisjs4  38693  isubgr0uhgr  47797
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