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Theorem nfsbxy 1818
 Description: Similar to hbsb 1823 but with an extra distinct variable constraint, on and . (Contributed by Jim Kingdon, 19-Mar-2018.)
Hypothesis
Ref Expression
nfsbxy.1
Assertion
Ref Expression
nfsbxy
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem nfsbxy
StepHypRef Expression
1 ax-bndl 1399 . 2
2 nfs1v 1815 . . . 4
3 drsb1 1680 . . . . 5
43drnf2 1622 . . . 4
52, 4mpbii 136 . . 3
6 a16nf 1746 . . . 4
7 df-nf 1350 . . . . . 6
87albii 1359 . . . . 5
9 sb5 1767 . . . . . 6
10 nfa1 1434 . . . . . . 7
11 sp 1401 . . . . . . . 8
12 nfsbxy.1 . . . . . . . . 9
1312a1i 9 . . . . . . . 8
1411, 13nfand 1460 . . . . . . 7
1510, 14nfexd 1644 . . . . . 6
169, 15nfxfrd 1364 . . . . 5
178, 16sylbir 125 . . . 4
186, 17jaoi 636 . . 3
195, 18jaoi 636 . 2
201, 19ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wo 629  wal 1241  wnf 1349  wex 1381  wsb 1645 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  nfsb  1822  sbalyz  1875  opelopabsb  3997
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