Theorem nfnfc1 2926

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 2910	. 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴)
2		nfnf1 2187	. . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴
3	2	nfal 2354	. 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴
4	1, 3	nfxfr 1881	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴

Syntax hints:  ∀wal 1566  Ⅎwnf 1811   ∈ wcel 2141  Ⅎwnfc 2908

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-10 2174  ax-11 2190  ax-12 2211

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1808  df-nf 1812  df-nfc 2910

This theorem is referenced by:  cbvexeqsetf  3468  sbcralt  3824  sbcrext  3825  csbiebt  3881  nfopd  4854  nfimad  6071  nffvd  6893  wl-issetft  38181  nfded  39687  nfded2  39688  nfunidALT2  39689