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 2191	. . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴
3	2	nfal 2354	. 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴
4	1, 3	nfxfr 1886	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴

This proof depends on syntax axioms:  ∀wal 1568  Ⅎwnf 1816   ∈ wcel 2145  Ⅎwnfc 2908

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2178  ax-11 2194  ax-12 2213

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817  df-nfc 2910

This theorem is used by:  cbvexeqsetf  3466  sbcralt  3819  sbcrext  3820  csbiebt  3876  nfopd  4850  nfimad  6065  nffvd  6897  wl-issetft  38514  nfded  40024  nfded2  40025  nfunidALT2  40026