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Theorem ax9 1949
Description: Theorem showing that ax-9 1662 follows from the weaker version ax9v 1663. (Even though this theorem depends on ax-9 1662, all references of ax-9 1662 are made via ax9v 1663. An earlier version stated ax9v 1663 as a separate axiom, but having two axioms caused some confusion.)

This theorem should be referenced in place of ax-9 1662 so that all proofs can be traced back to ax9v 1663. (Contributed by NM, 12-Nov-2013.) (Revised by NM, 25-Jul-2015.) (Proof shortened by Wolf Lammen, 4-Feb-2018.)

Assertion
Ref Expression
ax9  |-  -.  A. x  -.  x  =  y

Proof of Theorem ax9
StepHypRef Expression
1 a9e 1948 . 2  |-  E. x  x  =  y
2 df-ex 1548 . 2  |-  ( E. x  x  =  y  <->  -.  A. x  -.  x  =  y )
31, 2mpbi 200 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1546   E.wex 1547
This theorem is referenced by:  ax9o  1950  a9eOLD  2000  ax4567to4  27470
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548
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