Theorem nfnfc1 2909

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 2888	. 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴)
2		nfnf1 2153	. . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴
3	2	nfal 2321	. 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴
4	1, 3	nfxfr 1856	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴

Syntax hints:  ∀wal 1537  Ⅎwnf 1787   ∈ wcel 2108  Ⅎwnfc 2886

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2139  ax-11 2156  ax-12 2173

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-ex 1784  df-nf 1788  df-nfc 2888

This theorem is referenced by:  vtoclgft  3482  sbcralt  3801  sbcrext  3802  csbiebt  3858  nfopd  4818  nfimad  5967  nffvd  6768  nfded  36908  nfded2  36909  nfunidALT2  36910