Theorem nfcvfOLD 3009

Description: Obsolete version of nfcvf 3007 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 2977	. 2 ⊢ Ⅎ𝑥𝑧
2		nfcv 2977	. 2 ⊢ Ⅎ𝑧𝑦
3		id 22	. 2 ⊢ (𝑧 = 𝑦 → 𝑧 = 𝑦)
4	1, 2, 3	dvelimc 3006	1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥𝑦)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1535  Ⅎwnfc 2961

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-13 2390  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-cleq 2814  df-clel 2893  df-nfc 2963

This theorem is referenced by: (None)