Theorem nfald2 2073

Description: Variation on nfald 1951 which adds the hypothesis that and are distinct in the inner subproof. (Contributed by Mario Carneiro, 8-Oct-2016.)

Hypotheses

Ref	Expression
nfald2.1
nfald2.2

Assertion

Ref	Expression
nfald2

Proof of Theorem nfald2

Step	Hyp	Ref	Expression
1		nfald2.1	. . . . 5
2		nfnae 2058	. . . . 5
3	1, 2	nfan 1928	. . . 4
4		nfald2.2	. . . 4
5	3, 4	nfald 1951	. . 3
6	5	ex 434	. 2
7		nfa1 1897	. . 3
8		biidd 237	. . . 4
9	8	drnf1 2071	. . 3
10	7, 9	mpbiri 233	. 2
11	6, 10	pm2.61d2 160	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616

This theorem is referenced by:  nfexd2  2074  dvelimf  2076  nfeud2  2296  nfrald  2842  nfiotad  5559  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

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