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Theorem nfcvfOLD 3006
Description: Obsolete version of nfcvf 3004 as of 10-May-2023. (Contributed by Mario Carneiro, 8-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nfcvfOLD (¬ ∀𝑥 𝑥 = 𝑦𝑥𝑦)

Proof of Theorem nfcvfOLD
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 nfcv 2974 . 2 𝑥𝑧
2 nfcv 2974 . 2 𝑧𝑦
3 id 22 . 2 (𝑧 = 𝑦𝑧 = 𝑦)
41, 2, 3dvelimc 3003 1 (¬ ∀𝑥 𝑥 = 𝑦𝑥𝑦)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1526  wnfc 2958
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-13 2381  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-cleq 2811  df-clel 2890  df-nfc 2960
This theorem is referenced by: (None)
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