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Theorem sbal 1973
 Description: Move universal quantifier in and out of substitution. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 12-Feb-2018.)
Assertion
Ref Expression
sbal
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbal
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbalyz 1972 . . . 4
21sbbii 1738 . . 3
3 sbalyz 1972 . . 3
42, 3bitri 183 . 2
5 ax-17 1506 . . 3
65sbco2vh 1916 . 2
7 ax-17 1506 . . . 4
87sbco2vh 1916 . . 3
98albii 1446 . 2
104, 6, 93bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   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:  sbal1  1975  sbalv  1978  sbcal  2955  sbcalg  2956
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