Theorem nfceqi 2615

Description: Equality theorem for class not-free. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.)

Hypothesis

Ref	Expression
nfceqi.1

Assertion

Ref	Expression
nfceqi

Proof of Theorem nfceqi

Step	Hyp	Ref	Expression
1		nftru 1626	. . 3
2		nfceqi.1	. . . 4
3	2	a1i 11	. . 3
4	1, 3	nfceqdf 2614	. 2
5	4	trud 1404	1

Syntax hints:  <->wb 184  =wceq 1395  wtru 1396  F/_wnfc 2605

This theorem is referenced by:  nfcxfr  2617  nfcxfrd  2618

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607