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Theorem hbae 1560
 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 1365 . . . 4
2 ax10o 1557 . . . . . 6
32alequcoms 1371 . . . . 5
4 ax10o 1557 . . . . . . . . 9
54pm2.43i 41 . . . . . . . 8
6 ax10o 1557 . . . . . . . 8
75, 6syl5 26 . . . . . . 7
87alequcoms 1371 . . . . . 6
9 ax-4 1362 . . . . . . . 8
109imim1i 52 . . . . . . 7
1110sps 1393 . . . . . 6
128, 11jaoi 618 . . . . 5
133, 12jaoi 618 . . . 4
141, 13ax-mp 7 . . 3
1514a5i 1398 . 2
16 ax-7 1296 . 2
1715, 16syl 13 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 611  wal 1294   wceq 1353 This theorem is referenced by:  nfae  1561  hbaes  1562  hbnae  1563  dral1  1571  dral2  1572  drex2  1573  drex1  1632  aev  1646  sbcomxyyz  1795  exists1  1940 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 612  ax-5 1295  ax-7 1296  ax-gen 1297  ax-ie2 1343  ax-8 1357  ax-10 1358  ax-11 1359  ax-i12 1360  ax-4 1362  ax-17 1381  ax-i9 1385  ax-ial 1390 This theorem depends on definitions:  df-bi 108
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