Theorem axc9 2046

Description: Derive set.mm's original ax-c9 2221 from the shorter ax-13 1999. (Contributed by NM, 29-Nov-2015.) (Revised by NM, 24-Dec-2015.) (Proof shortened by Wolf Lammen, 29-Apr-2018.)

Assertion

Ref	Expression
axc9

Proof of Theorem axc9

Step	Hyp	Ref	Expression
1		nfeqf 2045	. . 3
2	1	nfrd 1875	. 2
3	2	ex 434	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393

This theorem is referenced by:  ax13  2047  hbae  2055  ax12eq  2271  ax12indalem  2275  axi12  2433  axbnd  2434  axext4dist  29233  wl-aleq  29988  bj-hbaeb2  34391

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-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617