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Theorem nfcvfOLD 2953
 Description: Obsolete version of nfcvf 2951 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 2925 . 2 𝑥𝑧
2 nfcv 2925 . 2 𝑧𝑦
3 id 22 . 2 (𝑧 = 𝑦𝑧 = 𝑦)
41, 2, 3dvelimc 2950 1 (¬ ∀𝑥 𝑥 = 𝑦𝑥𝑦)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1506  Ⅎwnfc 2909 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929  ax-7 1966  ax-8 2053  ax-9 2060  ax-10 2080  ax-11 2094  ax-12 2107  ax-13 2302  ax-ext 2743 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 835  df-tru 1511  df-ex 1744  df-nf 1748  df-cleq 2764  df-clel 2839  df-nfc 2911 This theorem is referenced by: (None)
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