Theorem axrep4 4567

Description: A more traditional version of the Axiom of Replacement. (Contributed by NM, 14-Aug-1994.)

Hypothesis

Ref	Expression
axrep4.1

Assertion

Ref	Expression
axrep4

Distinct variable group:   ,,,

Proof of Theorem axrep4

Step	Hyp	Ref	Expression
1		axrep3 4566	. . 3
2	1	19.35i 1689	. 2
3		nfv 1707	. . . . 5
4		nfv 1707	. . . . . . 7
5		nfa1 1897	. . . . . . 7
6	4, 5	nfan 1928	. . . . . 6
7	6	nfex 1948	. . . . 5
8	3, 7	nfbi 1934	. . . 4
9	8	nfal 1947	. . 3
10		nfv 1707	. . . . 5
11		nfe1 1840	. . . . 5
12	10, 11	nfbi 1934	. . . 4
13	12	nfal 1947	. . 3
14		elequ2 1823	. . . . 5
15		axrep4.1	. . . . . . . . 9
16	15	19.3 1888	. . . . . . . 8
17	16	anbi2i 694	. . . . . . 7
18	17	exbii 1667	. . . . . 6
19	18	a1i 11	. . . . 5
20	14, 19	bibi12d 321	. . . 4
21	20	albidv 1713	. . 3
22	9, 13, 21	cbvex 2022	. 2
23	2, 22	sylib 196	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616

This theorem is referenced by:  axrep5  4568  funimaexg  5670

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