Theorem ax-9 1519

Description: Derive ax-9 1519 from ax-i9 1518, the modified version for intuitionistic logic. Although ax-9 1519 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1518. (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 1518	. . 3 |- E. x x = y
2	1	notnoti 635	. 2 |- -. -. E. x x = y
3		alnex 1487	. 2 |- ( A. x -. x = y <-> -. E. x x = y )
4	2, 3	mtbir 661	1 |- -. A. x -. x = y

Syntax hints:   -. wn 3   A.wal 1341   = wceq 1343   E.wex 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1435  ax-gen 1437  ax-ie2 1482  ax-i9 1518

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349

This theorem is referenced by:  equidqe  1520