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Theorem rabbiiaOLD 3431
Description: Obsolete version of rabbiia 3430 as of 12-Jan-2025. (Contributed by NM, 22-May-1999.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
rabbiia.1 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
rabbiiaOLD {𝑥𝐴𝜑} = {𝑥𝐴𝜓}

Proof of Theorem rabbiiaOLD
StepHypRef Expression
1 rabbiia.1 . . . 4 (𝑥𝐴 → (𝜑𝜓))
21pm5.32i 574 . . 3 ((𝑥𝐴𝜑) ↔ (𝑥𝐴𝜓))
32abbii 2796 . 2 {𝑥 ∣ (𝑥𝐴𝜑)} = {𝑥 ∣ (𝑥𝐴𝜓)}
4 df-rab 3427 . 2 {𝑥𝐴𝜑} = {𝑥 ∣ (𝑥𝐴𝜑)}
5 df-rab 3427 . 2 {𝑥𝐴𝜓} = {𝑥 ∣ (𝑥𝐴𝜓)}
63, 4, 53eqtr4i 2764 1 {𝑥𝐴𝜑} = {𝑥𝐴𝜓}
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 395   = wceq 1533  wcel 2098  {cab 2703  {crab 3426
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-rab 3427
This theorem is referenced by: (None)
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