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Theorem sbal1yz 1976
 Description: Lemma for proving sbal1 1977. Same as sbal1 1977 but with an additional disjoint variable condition on . (Contributed by Jim Kingdon, 23-Feb-2018.)
Assertion
Ref Expression
sbal1yz
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbal1yz
StepHypRef Expression
1 dveeq2or 1788 . . . . . 6
2 equcom 1682 . . . . . . . . 9
32nfbii 1449 . . . . . . . 8
4 19.21t 1561 . . . . . . . 8
53, 4sylbi 120 . . . . . . 7
65orim2i 750 . . . . . 6
71, 6ax-mp 5 . . . . 5
87ori 712 . . . 4
98albidv 1796 . . 3
10 alcom 1454 . . . 4
11 sb6 1858 . . . . . 6
122imbi1i 237 . . . . . . 7
1312albii 1446 . . . . . 6
1411, 13bitri 183 . . . . 5
1514albii 1446 . . . 4
1610, 15bitr4i 186 . . 3
17 sb6 1858 . . . 4
182imbi1i 237 . . . . 5
1918albii 1446 . . . 4
2017, 19bitr2i 184 . . 3
219, 16, 203bitr3g 221 . 2
2221bicomd 140 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104   wo 697  wal 1329  wnf 1436  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-in2 604  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-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  1977
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