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Theorem nfceqi 2760
Description: Equality theorem for class not-free. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.)
Hypothesis
Ref Expression
nfceqi.1 𝐴 = 𝐵
Assertion
Ref Expression
nfceqi (𝑥𝐴𝑥𝐵)

Proof of Theorem nfceqi
StepHypRef Expression
1 nftru 1729 . . 3 𝑥
2 nfceqi.1 . . . 4 𝐴 = 𝐵
32a1i 11 . . 3 (⊤ → 𝐴 = 𝐵)
41, 3nfceqdf 2759 . 2 (⊤ → (𝑥𝐴𝑥𝐵))
54trud 1492 1 (𝑥𝐴𝑥𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 196   = wceq 1482  wtru 1483  wnfc 2750
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-12 2046  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1485  df-ex 1704  df-nf 1709  df-cleq 2614  df-clel 2617  df-nfc 2752
This theorem is referenced by:  nfcxfr  2761  nfcxfrd  2762
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