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Theorem nfald2 2060
 Description: Variation on nfald 1871 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
StepHypRef Expression
1 nfald2.1 . . . . 5
2 nfnae 2044 . . . . 5
31, 2nfan 1846 . . . 4
4 nfald2.2 . . . 4
53, 4nfald 1871 . . 3
65ex 424 . 2
7 nfa1 1806 . . 3
8 biidd 229 . . . 4
98drnf1 2057 . . 3
107, 9mpbiri 225 . 2
116, 10pm2.61d2 154 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wnf 1553 This theorem is referenced by:  nfexd2  2061  dvelimf  2064  dvelimfOLD  2065  nfeud2  2292  nfrald  2749  nfiotad  5413  nfixp  7073 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554
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