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Theorem equidqe 1466
Description: equid 1630 with some quantification and negation without using ax-4 1441 or ax-17 1460. (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 27-Feb-2014.)
Assertion
Ref Expression
equidqe  |-  -.  A. y  -.  x  =  x

Proof of Theorem equidqe
StepHypRef Expression
1 ax-9 1465 . 2  |-  -.  A. y  -.  y  =  x
2 ax-8 1436 . . . . 5  |-  ( y  =  x  ->  (
y  =  x  ->  x  =  x )
)
32pm2.43i 48 . . . 4  |-  ( y  =  x  ->  x  =  x )
43con3i 595 . . 3  |-  ( -.  x  =  x  ->  -.  y  =  x
)
54alimi 1385 . 2  |-  ( A. y  -.  x  =  x  ->  A. y  -.  y  =  x )
61, 5mto 621 1  |-  -.  A. y  -.  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-8 1436  ax-i9 1464
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291
This theorem is referenced by:  ax4sp1  1467
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