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Theorem sbalyz 1872
Description: Move universal quantifier in and out of substitution. Identical to sbal 1873 except that it has an additional distinct variable constraint on and . (Contributed by Jim Kingdon, 29-Dec-2017.)
Assertion
Ref Expression
sbalyz
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem sbalyz
StepHypRef Expression
1 nfa1 1431 . . . 4  F/
21nfsbxy 1815 . . 3  F/
3 ax-4 1397 . . . 4
43sbimi 1644 . . 3
52, 4alrimi 1412 . 2
6 sb6 1763 . . . . 5
76albii 1356 . . . 4
8 alcom 1364 . . . 4
97, 8bitri 173 . . 3
10 nfv 1418 . . . . . 6  F/
1110stdpc5 1473 . . . . 5
1211alimi 1341 . . . 4
13 sb2 1647 . . . 4
1412, 13syl 14 . . 3
159, 14sylbi 114 . 2
165, 15impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240  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  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  sbal  1873
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