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Theorem abeq12 33582
Description: Equality deduction for class abstraction. (Contributed by Giovanni Mascellani, 10-Apr-2018.)
Assertion
Ref Expression
abeq12 (∀𝑥(𝜑𝜓) → {𝑥𝜑} = {𝑥𝜓})

Proof of Theorem abeq12
StepHypRef Expression
1 abbi 2740 . 2 (∀𝑥(𝜑𝜓) ↔ {𝑥𝜑} = {𝑥𝜓})
21biimpi 206 1 (∀𝑥(𝜑𝜓) → {𝑥𝜑} = {𝑥𝜓})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1478   = wceq 1480  {cab 2612
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622
This theorem is referenced by: (None)
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