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Theorem nfceqiOLD 2946
 Description: Obsolete proof of nfceqi 2945 as of 19-Jun-2023. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfcxfr.1 𝐴 = 𝐵
Assertion
Ref Expression
nfceqiOLD (𝑥𝐴𝑥𝐵)

Proof of Theorem nfceqiOLD
StepHypRef Expression
1 nftru 1786 . . 3 𝑥
2 nfcxfr.1 . . . 4 𝐴 = 𝐵
32a1i 11 . . 3 (⊤ → 𝐴 = 𝐵)
41, 3nfceqdf 2944 . 2 (⊤ → (𝑥𝐴𝑥𝐵))
54mptru 1529 1 (𝑥𝐴𝑥𝐵)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 207   = wceq 1522  ⊤wtru 1523  Ⅎwnfc 2933 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-8 2083  ax-9 2091  ax-12 2141  ax-ext 2769 This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1525  df-ex 1762  df-nf 1766  df-cleq 2788  df-clel 2863  df-nfc 2935 This theorem is referenced by: (None)
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