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Theorem equidqe 1422
Description: equid 1586 with some quantification and negation without using ax-4 1397 or ax-17 1416. (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 27-Feb-2014.)
Assertion
Ref Expression
equidqe

Proof of Theorem equidqe
StepHypRef Expression
1 ax-9 1421 . 2
2 ax-8 1392 . . . . 5
32pm2.43i 43 . . . 4
43con3i 561 . . 3
54alimi 1341 . 2
61, 5mto 587 1
Colors of variables: wff set class
Syntax hints:   wn 3  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-i9 1420
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by:  ax4sp1  1423
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