Theorem nfifd 3969

Description: Deduction version of nfif 3970. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 13-Oct-2016.)

Hypotheses

Ref	Expression
nfifd.2
nfifd.3
nfifd.4

Assertion

Ref	Expression
nfifd

Proof of Theorem nfifd

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfif2 3943	. 2
2		nfv 1707	. . 3
3		nfifd.4	. . . . . 6
4	3	nfcrd 2625	. . . . 5
5		nfifd.2	. . . . 5
6	4, 5	nfimd 1917	. . . 4
7		nfifd.3	. . . . . 6
8	7	nfcrd 2625	. . . . 5
9	8, 5	nfand 1925	. . . 4
10	6, 9	nfimd 1917	. . 3
11	2, 10	nfabd 2641	. 2
12	1, 11	nfcxfrd 2618	1

Syntax hints:  ->wi 4  /\wa 369  F/wnf 1616  e.wcel 1818  {cab 2442  F/_wnfc 2605  ifcif 3941

This theorem is referenced by:  nfif  3970

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-or 370  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-if 3942