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Theorem ax9from9o 1816
Description: Rederivation of axiom ax-9 1684 from the orginal version, ax-9o 1815. See ax9o 1814 for the derivation of ax-9o 1815 from ax-9 1684. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint).

This theorem should not be referenced in any proof. Instead, use ax-9 1684 above so that uses of ax-9 1684 can be more easily identified. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion
Ref Expression
ax9from9o  |-  -.  A. x  -.  x  =  y

Proof of Theorem ax9from9o
StepHypRef Expression
1 ax-9o 1815 . 2  |-  ( A. x ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )  ->  -.  A. x  -.  x  =  y )
2 modal-b 1757 . 2  |-  ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )
31, 2mpg 1542 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1532
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-6 1534  ax-gen 1536  ax-4 1692  ax-9o 1815
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