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Theorem sbalyz 1972
 Description: Move universal quantifier in and out of substitution. Identical to sbal 1973 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 1521 . . . 4
21nfsbxy 1913 . . 3
3 ax-4 1487 . . . 4
43sbimi 1737 . . 3
52, 4alrimi 1502 . 2
6 sb6 1858 . . . . 5
76albii 1446 . . . 4
8 alcom 1454 . . . 4
97, 8bitri 183 . . 3
10 nfv 1508 . . . . . 6
1110stdpc5 1563 . . . . 5
1211alimi 1431 . . . 4
13 sb2 1740 . . . 4
1412, 13syl 14 . . 3
159, 14sylbi 120 . 2
165, 15impbii 125 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1329  wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736 This theorem is referenced by:  sbal  1973
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