Theorem ax-9 1424

Description: Derive ax-9 1424 from ax-i9 1423, the modified version for intuitionistic logic. Although ax-9 1424 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1423. (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 1423	. . 3 |- E. x x = y
2	1	notnoti 574	. 2 |- -. -. E. x x = y
3		alnex 1388	. 2 |- ( A. x -. x = y <-> -. E. x x = y )
4	2, 3	mtbir 596	1 |- -. A. x -. x = y

Syntax hints:   -. wn 3   A.wal 1241   = wceq 1243   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-i9 1423

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  equidqe  1425