Theorem cleqf 2646

Description: Establish equality between classes, using bound-variable hypotheses instead of distinct variable conditions. See also cleqh 2572. (Contributed by NM, 26-May-1993.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof shortened by Wolf Lammen, 17-Nov-2019.)

Hypotheses

Ref	Expression
cleqf.1
cleqf.2

Assertion

Ref	Expression
cleqf

Proof of Theorem cleqf

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		cleqf.1	. . 3
2	1	nfcrii 2611	. 2
3		cleqf.2	. . 3
4	3	nfcrii 2611	. 2
5	2, 4	cleqh 2572	1

Syntax hints:  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  F/_wnfc 2605

This theorem is referenced by:  abid2f  2648  abid2fOLD  2649  n0f  3793  iunab  4376  iinab  4391  mbfposr  22059  mbfinf  22072  itg1climres  22121  compab  31350  bnj1366  33888  bj-rabtrALT  34498

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607