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Theorem hbae 1696
 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 1490 . . . 4
2 ax10o 1693 . . . . . 6
32alequcoms 1496 . . . . 5
4 ax10o 1693 . . . . . . . . 9
54pm2.43i 49 . . . . . . . 8
6 ax10o 1693 . . . . . . . 8
75, 6syl5 32 . . . . . . 7
87alequcoms 1496 . . . . . 6
9 ax-4 1487 . . . . . . . 8
109imim1i 60 . . . . . . 7
1110sps 1517 . . . . . 6
128, 11jaoi 705 . . . . 5
133, 12jaoi 705 . . . 4
141, 13ax-mp 5 . . 3
1514a5i 1522 . 2
16 ax-7 1424 . 2
1715, 16syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 697  wal 1329   wceq 1331 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  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 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  nfae  1697  hbaes  1698  hbnae  1699  dral1  1708  dral2  1709  drex2  1710  drex1  1770  aev  1784  sbcomxyyz  1943  exists1  2093
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