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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
StepHypRef Expression
1 nfald2.1 . . . . 5
2 nfnae 2058 . . . . 5
31, 2nfan 1928 . . . 4
4 nfald2.2 . . . 4
53, 4nfald 1951 . . 3
65ex 434 . 2
7 nfa1 1897 . . 3
8 biidd 237 . . . 4
98drnf1 2071 . . 3
107, 9mpbiri 233 . 2
116, 10pm2.61d2 160 1
 Colors of variables: wff setvar class 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
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