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Theorem ax9from9o 2100
Description: Rederivation of axiom ax-9 1644 from ax-9o 2090 and other older axioms. See ax9o 1903 for the derivation of ax-9o 2090 from ax-9 1644. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint). (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 2090 . 2  |-  ( A. x ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )  ->  -.  A. x  -.  x  =  y )
2 ax-6o 2089 . . 3  |-  ( -. 
A. x  -.  A. x  -.  x  =  y  ->  -.  x  =  y )
32con4i 122 . 2  |-  ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )
41, 3mpg 1538 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
This theorem is referenced by:  equidqe  2125
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-6o 2089  ax-9o 2090
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