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Theorem rabbiia 2849
Description: Equivalent wff's yield equal restricted class abstractions (inference rule). (Contributed by NM, 22-May-1999.)
Hypothesis
Ref Expression
rabbiia.1 (x A → (φψ))
Assertion
Ref Expression
rabbiia {x A φ} = {x A ψ}

Proof of Theorem rabbiia
StepHypRef Expression
1 rabbiia.1 . . . 4 (x A → (φψ))
21pm5.32i 618 . . 3 ((x A φ) ↔ (x A ψ))
32abbii 2465 . 2 {x (x A φ)} = {x (x A ψ)}
4 df-rab 2623 . 2 {x A φ} = {x (x A φ)}
5 df-rab 2623 . 2 {x A ψ} = {x (x A ψ)}
63, 4, 53eqtr4i 2383 1 {x A φ} = {x A ψ}
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358   = wceq 1642   wcel 1710  {cab 2339  {crab 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-rab 2623
This theorem is referenced by: (None)
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