Theorem nfcvf2 2513

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 2512	. 2 ⊢ (¬ ∀y y = x → Ⅎyx)
2	1	naecoms 1948	1 ⊢ (¬ ∀x x = y → Ⅎyx)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnfc 2477

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This proof depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2479

This theorem is used by:  dfid3  4769  oprabid  5551