Theorem nfnfc1 2905

Description: The setvar 𝑥 is bound in Ⅎ𝑥𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnfc1	⊢ Ⅎ𝑥Ⅎ𝑥𝐴

Proof of Theorem nfnfc1

Dummy variable 𝑦 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nfc 2884	. 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴)
2		nfnf1 2150	. . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴
3	2	nfal 2315	. 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴
4	1, 3	nfxfr 1854	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴

Syntax hints:  ∀wal 1538  Ⅎwnf 1784   ∈ wcel 2105  Ⅎwnfc 2882

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 1912  ax-6 1970  ax-7 2010  ax-10 2136  ax-11 2153  ax-12 2170

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-ex 1781  df-nf 1785  df-nfc 2884

This theorem is referenced by:  issetft  3487  sbcralt  3866  sbcrext  3867  csbiebt  3923  nfopd  4890  nfimad  6068  nffvd  6903  wl-issetft  36908  nfded  38301  nfded2  38302  nfunidALT2  38303