Theorem ax9 1165

Description: Rederivation of axiom ax-9 1006 from the orginal version, ax-9o 1164. See ax9o 1163 for the derivation of ax-9o 1164 from ax-9 1006. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint).

This theorem should not be referenced in any proof. Instead, use ax-9 1006 above so that uses of ax-9 1006 can be more easily identified.

Assertion

Ref	Expression
ax9	|- -. A.x -. x = y

Proof of Theorem ax9

Step	Hyp	Ref	Expression
1		ax-9o 1164	. 2 |- (A.x(x = y -> A.x -. A.x -. x = y) -> -. A.x -. x = y)
2		modal-b 1069	. 2 |- (x = y -> A.x -. A.x -. x = y)
3	1, 2	mpg 1027	1 |- -. A.x -. x = y

Syntax hints:  -. wn 2   -> wi 3  A.wal 995   = wceq 997

This theorem was proved from axioms:  ax-3 6  ax-mp 7  ax-gen 1004  ax-6o 1019  ax-9o 1164

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