Theorem rexraleqim 3225

Description: Statement following from existence and generalization with equality. (Contributed by AV, 9-Feb-2019.)

Hypotheses

Ref	Expression
rexraleqim.1
rexraleqim.2

Assertion

Ref	Expression
rexraleqim

Distinct variable groups:   ,,   ,,   ,   ,   ,

Proof of Theorem rexraleqim

Step	Hyp	Ref	Expression
1		rexraleqim.1	. . . . . . 7
2		eqeq1 2461	. . . . . . 7
3	1, 2	imbi12d 320	. . . . . 6
4	3	rspcva 3208	. . . . 5
5		rexraleqim.2	. . . . . 6
6	5	biimpd 207	. . . . 5
7	4, 6	syli 37	. . . 4
8	7	impancom 440	. . 3
9	8	rexlimiva 2945	. 2
10	9	imp 429	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808

This theorem is referenced by:  cramerlem3  19191

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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111