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Axiom ax-9o 2082
Description: A variant of ax9 1893. Axiom scheme C10' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is obsolete and should no longer be used. It is proved above as theorem ax9o 1894. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion
Ref Expression
ax-9o  |-  ( A. x ( x  =  y  ->  A. x ph )  ->  ph )

Detailed syntax breakdown of Axiom ax-9o
StepHypRef Expression
1 vx . . . . 5  set  x
2 vy . . . . 5  set  y
31, 2weq 1626 . . . 4  wff  x  =  y
4 wph . . . . 5  wff  ph
54, 1wal 1529 . . . 4  wff  A. x ph
63, 5wi 6 . . 3  wff  ( x  =  y  ->  A. x ph )
76, 1wal 1529 . 2  wff  A. x
( x  =  y  ->  A. x ph )
87, 4wi 6 1  wff  ( A. x ( x  =  y  ->  A. x ph )  ->  ph )
Colors of variables: wff set class
This axiom is referenced by:  ax9from9o  2091  equid1  2101  equid1ALT  2119
  Copyright terms: Public domain W3C validator