Theorem nfabd2 2640

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
nfabd2.1
nfabd2.2

Assertion

Ref	Expression
nfabd2

Proof of Theorem nfabd2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfv 1707	. . . 4
2		df-clab 2443	. . . . 5
3		nfabd2.1	. . . . . . 7
4		nfnae 2058	. . . . . . 7
5	3, 4	nfan 1928	. . . . . 6
6		nfabd2.2	. . . . . 6
7	5, 6	nfsbd 2186	. . . . 5
8	2, 7	nfxfrd 1646	. . . 4
9	1, 8	nfcd 2613	. . 3
10	9	ex 434	. 2
11		nfab1 2621	. . 3
12		eqidd 2458	. . . 4
13	12	drnfc1 2638	. . 3
14	11, 13	mpbiri 233	. 2
15	10, 14	pm2.61d2 160	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616  [wsb 1739  e.wcel 1818  {cab 2442  F/_wnfc 2605

This theorem is referenced by:  nfabd  2641  nfrab  3039  nfixp  7508

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-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607