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Theorem hbae 2055
 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 1859 . . . . 5
2 axc9 2046 . . . . 5
31, 2syl7 68 . . . 4
4 axc112 1937 . . . 4
5 axc11 2054 . . . . . 6
65pm2.43i 47 . . . . 5
7 axc112 1937 . . . . 5
86, 7syl5 32 . . . 4
93, 4, 8pm2.61ii 165 . . 3
109axc4i 1898 . 2
11 ax-11 1842 . 2
1210, 11syl 16 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  A.wal 1393 This theorem is referenced by:  nfae  2056  hbnae  2057  aevALT  2063  drex2  2070  ax6e2eq  33330 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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