Theorem ax9 1120

Description: Rederivation of axiom ax-9 962 from the orginal version, ax-9o 1119. See ax9o 1118 for the derivation of ax-9o 1119 from ax-9 962. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint).

This theorem should not be referenced in any proof. Instead, use ax-9 962 above so that uses of ax-9 962 can be more easily identified.

Assertion

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

Proof of Theorem ax9

Step	Hyp	Ref	Expression
1		ax-9o 1119	. 2 |- (A.x(x = y -> A.x -. A.x -. x = y) -> -. A.x -. x = y)
2		modal-b 1024	. 2 |- (x = y -> A.x -. A.x -. x = y)
3	1, 2	mpg 983	1 |- -. A.x -. x = y

Syntax hints:  -. wn 2   -> wi 3  A.wal 951   = wceq 953

This theorem was proved from axioms:  ax-3 6  ax-mp 7  ax-gen 960  ax-6o 975  ax-9o 1119

Copyright terms: Public domain