Theorem ax-9 1494

Description: Derive ax-9 1494 from ax-i9 1493, the modified version for intuitionistic logic. Although ax-9 1494 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1493. (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 1493	. . 3 |- E. x x = y
2	1	notnoti 617	. 2 |- -. -. E. x x = y
3		alnex 1458	. 2 |- ( A. x -. x = y <-> -. E. x x = y )
4	2, 3	mtbir 643	1 |- -. A. x -. x = y

Syntax hints:   -. wn 3   A.wal 1312   = wceq 1314   E.wex 1451

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-ie2 1453  ax-i9 1493

This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320

This theorem is referenced by:  equidqe  1495