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Theorem ax9from9o 2089
Description: Rederivation of axiom ax-9 1637 from ax-9o 2080 and other older axioms. See ax9o 1891 for the derivation of ax-9o 2080 from ax-9 1637. 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 2080 . 2  |-  ( A. x ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )  ->  -.  A. x  -.  x  =  y )
2 ax-6o 2079 . . 3  |-  ( -. 
A. x  -.  A. x  -.  x  =  y  ->  -.  x  =  y )
32con4i 124 . 2  |-  ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )
41, 3mpg 1536 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1528
This theorem is referenced by:  equidqe  2114
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-6o 2079  ax-9o 2080
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