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Theorem nfcvf2 2305
Description: If 𝑥 and 𝑦 are distinct, then 𝑦 is not free in 𝑥. (Contributed by Mario Carneiro, 5-Dec-2016.)
Assertion
Ref Expression
nfcvf2 (¬ ∀𝑥 𝑥 = 𝑦𝑦𝑥)

Proof of Theorem nfcvf2
StepHypRef Expression
1 nfcvf 2304 . 2 (¬ ∀𝑦 𝑦 = 𝑥𝑦𝑥)
21naecoms 1703 1 (¬ ∀𝑥 𝑥 = 𝑦𝑦𝑥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1330  wnfc 2269
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-cleq 2133  df-clel 2136  df-nfc 2271
This theorem is referenced by: (None)
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