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Theorem ax6fromc10 32437
Description: Rederivation of axiom ax-6 1798 from ax-c10 32427 and other older axioms. See axc10 2062 for the derivation of ax-c10 32427 from ax-6 1798. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 14-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax6fromc10  |-  -.  A. x  -.  x  =  y

Proof of Theorem ax6fromc10
StepHypRef Expression
1 ax-c10 32427 . 2  |-  ( A. x ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )  ->  -.  A. x  -.  x  =  y )
2 ax-c7 32426 . . 3  |-  ( -. 
A. x  -.  A. x  -.  x  =  y  ->  -.  x  =  y )
32con4i 133 . 2  |-  ( x  =  y  ->  A. x  -.  A. x  -.  x  =  y )
41, 3mpg 1665 1  |-  -.  A. x  -.  x  =  y
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-c7 32426  ax-c10 32427
This theorem is referenced by:  equidqe  32462
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