Theorem nfcvf2 2399

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 = 𝑦 → Ⅎ𝑦𝑥)

Proof of Theorem nfcvf2

Step	Hyp	Ref	Expression
1		nfcvf 2398	. 2 ⊢ (¬ ∀𝑦 𝑦 = 𝑥 → Ⅎ𝑦𝑥)
2	1	naecoms 1772	1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑦𝑥)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1396  Ⅎwnfc 2362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510  df-sb 1811  df-cleq 2224  df-clel 2227  df-nfc 2364

This theorem is referenced by: (None)