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Theorem hbae 1496
Description: All variables are effectively bound in an identical variable specifier. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.)
Assertion
Ref Expression
hbae

Proof of Theorem hbae
StepHypRef Expression
1 ax12or 1336 . . . 4
2 ax10o 1493 . . . . . 6
32alequcoms 1341 . . . . 5
4 ax10o 1493 . . . . . . . . 9
54pm2.43i 41 . . . . . . . 8
6 ax10o 1493 . . . . . . . 8
75, 6syl5 26 . . . . . . 7
87alequcoms 1341 . . . . . 6
9 ax-4 1333 . . . . . . . 8
109imim1i 52 . . . . . . 7
1110a4s 1362 . . . . . 6
128, 11jaoi 615 . . . . 5
133, 12jaoi 615 . . . 4
141, 13ax-mp 7 . . 3
1514a5i 1367 . 2
16 ax-7 1268 . 2
1715, 16syl 13 1
Colors of variables: wff set class
Syntax hints:   wi 4   wo 608  wal 1266   wceq 1324
This theorem is referenced by:  nfae  1497  hbaes  1498  hbnae  1499  dral1  1507  dral2  1508  drex2  1509  drex1  1565  aev  1579  sbcomxyyz  1723  exists1  2159
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-io 609  ax-5 1267  ax-7 1268  ax-gen 1269  ax-ie2 1315  ax-8 1328  ax-10 1329  ax-11 1330  ax-i12 1331  ax-4 1333  ax-17 1350  ax-i9 1354  ax-ial 1359
This theorem depends on definitions:  df-bi 108
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