Theorem ax-9 1464

Description: Derive ax-9 1464 from ax-i9 1463, the modified version for intuitionistic logic. Although ax-9 1464 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1463. (Contributed by NM, 3-Feb-2015.)

Assertion

Ref	Expression
ax-9	|- -. A. x -. x = y

Proof of Theorem ax-9

Step	Hyp	Ref	Expression
1		ax-i9 1463	. . 3 |- E. x x = y
2	1	notnoti 606	. 2 |- -. -. E. x x = y
3		alnex 1428	. 2 |- ( A. x -. x = y <-> -. E. x x = y )
4	2, 3	mtbir 628	1 |- -. A. x -. x = y

Syntax hints:   -. wn 3   A.wal 1282   = wceq 1284   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie2 1423  ax-i9 1463

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  equidqe  1465