Theorem dvelimdc 2642

Description: Deduction form of dvelimc 2643. (Contributed by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
dvelimdc.1
dvelimdc.2
dvelimdc.3
dvelimdc.4
dvelimdc.5

Assertion

Ref	Expression
dvelimdc

Proof of Theorem dvelimdc

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfv 1707	. . 3
2		dvelimdc.1	. . . . 5
3		dvelimdc.2	. . . . 5
4		dvelimdc.3	. . . . . 6
5	4	nfcrd 2625	. . . . 5
6		dvelimdc.4	. . . . . 6
7	6	nfcrd 2625	. . . . 5
8		dvelimdc.5	. . . . . 6
9		eleq2 2530	. . . . . 6
10	8, 9	syl6 33	. . . . 5
11	2, 3, 5, 7, 10	dvelimdf 2077	. . . 4
12	11	imp 429	. . 3
13	1, 12	nfcd 2613	. 2
14	13	ex 434	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605

This theorem is referenced by:  dvelimc  2643

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-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607