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Axiom ax-9o 1815
Description: A variant of ax-9 1684. Axiom scheme C10' in [Megill] p. 448 (p. 16 of the preprint).

This axiom is redundant, as shown by theorem ax9o 1814.

Normally, ax9o 1814 should be used rather than ax-9o 1815, except by theorems specifically studying the latter's properties. (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 1620 . . . 4  wff  x  =  y
4 wph . . . . 5  wff  ph
54, 1wal 1532 . . . 4  wff  A. x ph
63, 5wi 6 . . 3  wff  ( x  =  y  ->  A. x ph )
76, 1wal 1532 . 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  1816  equidALT  1819
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