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 2891	. 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴)
2		nfnf1 2180	. . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴
3	2	nfal 2300	. 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴
4	1, 3	nfxfr 1928	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴

Syntax hints:  ∀wal 1630  Ⅎwnf 1857   ∈ wcel 2139  Ⅎwnfc 2889

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-11 2183  ax-12 2196

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-nfc 2891

This theorem is referenced by:  vtoclgft  3394  vtoclgftOLD  3395  sbcralt  3651  sbcrext  3652  sbcrextOLD  3653  csbiebt  3694  nfopd  4570  nfimad  5633  nffvd  6361  nfded  34757  nfded2  34758  nfunidALT2  34759