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Theorem hbae 2149
 Description: All variables are effectively bound in an identical variable specifier. (Contributed by NM, 13-May-1993.) (Proof shortened by Wolf Lammen, 21-Apr-2018.)
Assertion
Ref Expression
hbae

Proof of Theorem hbae
StepHypRef Expression
1 sp 1937 . . . . 5
2 axc9 2140 . . . . 5
31, 2syl7 70 . . . 4
4 axc112 2020 . . . 4
5 axc11 2148 . . . . . 6
65pm2.43i 49 . . . . 5
7 axc112 2020 . . . . 5
86, 7syl5 33 . . . 4
93, 4, 8pm2.61ii 169 . . 3
109axc4i 1980 . 2
11 ax-11 1920 . 2
1210, 11syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1442 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668 This theorem is referenced by:  nfae  2150  hbnae  2151  aevALT  2155  drex2  2162  ax6e2eq  36924
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