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Theorem sbal1yz 1877
 Description: Lemma for proving sbal1 1878. Same as sbal1 1878 but with an additional distinct variable constraint on and . (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 1697 . . . . . 6
2 equcom 1593 . . . . . . . . 9
32nfbii 1362 . . . . . . . 8
4 19.21t 1474 . . . . . . . 8
53, 4sylbi 114 . . . . . . 7
65orim2i 678 . . . . . 6
71, 6ax-mp 7 . . . . 5
87ori 642 . . . 4
98albidv 1705 . . 3
10 alcom 1367 . . . 4
11 sb6 1766 . . . . . 6
122imbi1i 227 . . . . . . 7
1312albii 1359 . . . . . 6
1411, 13bitri 173 . . . . 5
1514albii 1359 . . . 4
1610, 15bitr4i 176 . . 3
17 sb6 1766 . . . 4
182imbi1i 227 . . . . 5
1918albii 1359 . . . 4
2017, 19bitr2i 174 . . 3
219, 16, 203bitr3g 211 . 2
2221bicomd 129 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 98   wo 629  wal 1241  wnf 1349  wsb 1645 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-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  sbal1  1878
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