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Theorem hbae 1841
 Description: All variables are effectively bound in an identical variable specifier. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbae

Proof of Theorem hbae
StepHypRef Expression
1 ax-4 1692 . . . . 5
2 ax-12o 1664 . . . . 5
31, 2syl7 65 . . . 4
4 ax10o 1835 . . . . 5
54alequcoms 1681 . . . 4
6 ax10o 1835 . . . . . . 7
76pm2.43i 45 . . . . . 6
8 ax10o 1835 . . . . . 6
97, 8syl5 30 . . . . 5
109alequcoms 1681 . . . 4
113, 5, 10pm2.61ii 159 . . 3
1211a5i 1721 . 2
13 ax-7 1535 . 2
1412, 13syl 17 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6  wal 1532 This theorem is referenced by:  nfae  1843  hbaes  1844  hbnae  1845  dral1  1856  dral2  1858  drex2  1861  a9e2eq  27360  a12stdy3  28279 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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