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Theorem nfsbxy 1815
Description: Similar to hbsb 1820 but with an extra distinct variable constraint, on and . (Contributed by Jim Kingdon, 19-Mar-2018.)
Hypothesis
Ref Expression
nfsbxy.1  F/
Assertion
Ref Expression
nfsbxy  F/
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem nfsbxy
StepHypRef Expression
1 ax-bnd 1396 . 2
2 nfs1v 1812 . . . 4  F/
3 drsb1 1677 . . . . 5
43drnf2 1619 . . . 4  F/  F/
52, 4mpbii 136 . . 3  F/
6 a16nf 1743 . . . 4  F/
7 df-nf 1347 . . . . . 6  F/
87albii 1356 . . . . 5  F/
9 sb5 1764 . . . . . 6
10 nfa1 1431 . . . . . . 7  F/ F/
11 sp 1398 . . . . . . . 8  F/  F/
12 nfsbxy.1 . . . . . . . . 9  F/
1312a1i 9 . . . . . . . 8  F/  F/
1411, 13nfand 1457 . . . . . . 7  F/  F/
1510, 14nfexd 1641 . . . . . 6  F/  F/
169, 15nfxfrd 1361 . . . . 5  F/  F/
178, 16sylbir 125 . . . 4  F/
186, 17jaoi 635 . . 3 
F/
195, 18jaoi 635 . 2 
F/
201, 19ax-mp 7 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 628  wal 1240   F/wnf 1346  wex 1378  wsb 1642
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  nfsb  1819  sbalyz  1872  opelopabsb  3988
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