NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nfald2 Unicode version

Theorem nfald2 1972
Description: Variation on nfald 1852 which adds the hypothesis that and are distinct in the inner subproof. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
nfald2.1  F/
nfald2.2  F/
Assertion
Ref Expression
nfald2  F/

Proof of Theorem nfald2
StepHypRef Expression
1 nfald2.1 . . . . 5  F/
2 nfnae 1956 . . . . 5  F/
31, 2nfan 1824 . . . 4  F/
4 nfald2.2 . . . 4  F/
53, 4nfald 1852 . . 3  F/
65ex 423 . 2  F/
7 nfa1 1788 . . 3  F/
8 biidd 228 . . . 4
98drnf1 1969 . . 3  F/  F/
107, 9mpbiri 224 . 2  F/
116, 10pm2.61d2 152 1  F/
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wa 358  wal 1540   F/wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  nfexd2  1973  dvelimf  1997  nfeud2  2216  nfrald  2665  nfiotad  4342
  Copyright terms: Public domain W3C validator