Theorem axrep3 4566

Description: Axiom of Replacement slightly strengthened from axrep2 4565; may occur free in . (Contributed by NM, 2-Jan-1997.)

Assertion

Ref	Expression
axrep3

Distinct variable group:   ,,,

Proof of Theorem axrep3

Step	Hyp	Ref	Expression
1		nfe1 1840	. . . 4
2		nfv 1707	. . . . . 6
3		nfv 1707	. . . . . . . 8
4		nfa1 1897	. . . . . . . 8
5	3, 4	nfan 1928	. . . . . . 7
6	5	nfex 1948	. . . . . 6
7	2, 6	nfbi 1934	. . . . 5
8	7	nfal 1947	. . . 4
9	1, 8	nfim 1920	. . 3
10	9	nfex 1948	. 2
11		elequ2 1823	. . . . . . . 8
12	11	anbi1d 704	. . . . . . 7
13	12	exbidv 1714	. . . . . 6
14	13	bibi2d 318	. . . . 5
15	14	albidv 1713	. . . 4
16	15	imbi2d 316	. . 3
17	16	exbidv 1714	. 2
18		axrep2 4565	. 2
19	10, 17, 18	chvar 2013	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612

This theorem is referenced by:  axrep4  4567

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-rep 4563

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617