Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfexd2 Structured version   Unicode version

Theorem nfexd2 2061
 Description: Variation on nfexd 1873 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
nfexd2

Proof of Theorem nfexd2
StepHypRef Expression
1 df-ex 1551 . 2
2 nfald2.1 . . . 4
3 nfald2.2 . . . . 5
43nfnd 1809 . . . 4
52, 4nfald2 2060 . . 3
65nfnd 1809 . 2
71, 6nfxfrd 1580 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  nfeud2  2292  nfmod2  2293 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
 Copyright terms: Public domain W3C validator