Theorem nfnfc1 2928

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 2912	. 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴)
2		nfnf1 2189	. . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴
3	2	nfal 2356	. 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴
4	1, 3	nfxfr 1883	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴

Syntax hints:  ∀wal 1568  Ⅎwnf 1813   ∈ wcel 2143  Ⅎwnfc 2910

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-10 2176  ax-11 2192  ax-12 2213

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1810  df-nf 1814  df-nfc 2912

This theorem is referenced by:  cbvexeqsetf  3470  sbcralt  3825  sbcrext  3826  csbiebt  3882  nfopd  4855  nfimad  6071  nffvd  6893  wl-issetft  38257  nfded  39761  nfded2  39762  nfunidALT2  39763