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Theorem rabbieq 3444
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 3441 . 2 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
41, 3eqtri 2764 1 𝐵 = {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1539  {crab 3435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-rab 3436
This theorem is referenced by:  dfdif3  4116  1arithufd  33577  dfrefrels3  38516  dfcnvrefrels3  38531  dfsymrels3  38548  refsymrels3  38568  dftrrels3  38578  dfeqvrels3  38591  dfdisjs3  38712  dfdisjs4  38713  isubgr0uhgr  47864
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