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Theorem sbal1yz 1874
Description: Lemma for proving sbal1 1875. Same as sbal1 1875 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 1694 . . . . . 6  F/
2 equcom 1590 . . . . . . . . 9
32nfbii 1359 . . . . . . . 8  F/  F/
4 19.21t 1471 . . . . . . . 8  F/
53, 4sylbi 114 . . . . . . 7  F/
65orim2i 677 . . . . . 6  F/
71, 6ax-mp 7 . . . . 5
87ori 641 . . . 4
98albidv 1702 . . 3
10 alcom 1364 . . . 4
11 sb6 1763 . . . . . 6
122imbi1i 227 . . . . . . 7
1312albii 1356 . . . . . 6
1411, 13bitri 173 . . . . 5
1514albii 1356 . . . 4
1610, 15bitr4i 176 . . 3
17 sb6 1763 . . . 4
182imbi1i 227 . . . . 5
1918albii 1356 . . . 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 628  wal 1240   F/wnf 1346  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-in2 545  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-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:  sbal1  1875
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