Theorem rexlimd2 2940

Description: Version of rexlimd 2941 with deduction version of second hypothesis. (Contributed by NM, 21-Jul-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
rexlimd2.1
rexlimd2.2
rexlimd2.3

Assertion

Ref	Expression
rexlimd2

Proof of Theorem rexlimd2

Step	Hyp	Ref	Expression
1		rexlimd2.1	. . 3
2		rexlimd2.3	. . 3
3	1, 2	ralrimi 2857	. 2
4		rexlimd2.2	. . 3
5		r19.23t 2935	. . 3
6	4, 5	syl 16	. 2
7	3, 6	mpbid 210	1

Syntax hints:  ->wi 4  <->wb 184  F/wnf 1616  e.wcel 1818  A.wral 2807  E.wrex 2808

This theorem is referenced by:  rexlimd  2941  sbcrext  3410

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813