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 = 𝑦 → Ⅎ𝑥𝑦)

Proof of Theorem nfcvfOLD

Dummy variable 𝑧 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfcv 2925	. 2 ⊢ Ⅎ𝑥𝑧
2		nfcv 2925	. 2 ⊢ Ⅎ𝑧𝑦
3		id 22	. 2 ⊢ (𝑧 = 𝑦 → 𝑧 = 𝑦)
4	1, 2, 3	dvelimc 2950	1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝑦)

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)