Theorem ax9 1482

Description: Rederivation of axiom ax-9 1307 from the orginal version, ax-9o 1481. See ax9o 1480 for the derivation of ax-9o 1481 from ax-9 1307. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint).

This theorem should not be referenced in any proof. Instead, use ax-9 1307 above so that uses of ax-9 1307 can be more easily identified.

Assertion

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

Proof of Theorem ax9

Step	Hyp	Ref	Expression
1		ax-9o 1481	. 2 |- (A.x(x = y -> A.x -. A.x -. x = y) -> -. A.x -. x = y)
2		modal-b 1375	. 2 |- (x = y -> A.x -. A.x -. x = y)
3	1, 2	mpg 1332	1 |- -. A.x -. x = y

Syntax hints:  -. wn 2   -> wi 3  A.wal 1296   = wceq 1298

This theorem was proved from axioms:  ax-3 6  ax-mp 7  ax-gen 1305  ax-6o 1324  ax-9o 1481

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