Theorem ax9a 1111

Description: This theorem is a re-derivation of ax-9 1102 from ax9 1110. This shows that ax-9 1102 and ax9 1110 are interchangeable in the presence of the other axioms. Lemma L18 in [Megill] p. 446 (p. 14 of the preprint). Use it instead of ax-9 1102 so we interchange ax-9 1102 and ax9 1110 as our axiom.

Assertion

Ref	Expression
ax9a	|- -. A.x -. x = y

Proof of Theorem ax9a

Step	Hyp	Ref	Expression
1		ax9 1110	. 2 |- (A.x(x = y -> A.x -. A.x -. x = y) -> -. A.x -. x = y)
2		modal-b 1004	. 2 |- (x = y -> A.x -. A.x -. x = y)
3	1, 2	mpg 962	1 |- -. A.x -. x = y

Syntax hints:  -. wn 2   -> wi 3  A.wal 950   = wceq 1099

This theorem is referenced by:  a9e 1112  a16g 1258

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-gen 955  ax-9 1102

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957

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