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Theorem nfcvf2 2933
Description: If 𝑥 and 𝑦 are distinct, then 𝑦 is not free in 𝑥. Usage of this theorem is discouraged because it depends on ax-13 2377. See nfcv 2905 for a version that replaces the distinctor with a disjoint variable condition, requiring fewer axioms. (Contributed by Mario Carneiro, 5-Dec-2016.) (New usage is discouraged.)
Assertion
Ref Expression
nfcvf2 (¬ ∀𝑥 𝑥 = 𝑦𝑦𝑥)

Proof of Theorem nfcvf2
StepHypRef Expression
1 nfcvf 2932 . 2 (¬ ∀𝑦 𝑦 = 𝑥𝑦𝑥)
21naecoms 2434 1 (¬ ∀𝑥 𝑥 = 𝑦𝑦𝑥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1538  wnfc 2890
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-13 2377
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-nfc 2892
This theorem is referenced by:  dfid3  5581  oprabid  7463  axrepndlem1  10632  axrepndlem2  10633  axrepnd  10634  axunnd  10636  axpowndlem3  10639  axpowndlem4  10640  axpownd  10641  axregndlem2  10643  axinfndlem1  10645  axinfnd  10646  axacndlem4  10650  axacndlem5  10651  axacnd  10652  bj-nfcsym  36900
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