Theorem ax-9 1554

Description: Derive ax-9 1554 from ax-i9 1553, the modified version for intuitionistic logic. Although ax-9 1554 does hold intuistionistically, in intuitionistic logic it is weaker than ax-i9 1553. (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 1553	. . 3 |- E. x x = y
2	1	notnoti 646	. 2 |- -. -. E. x x = y
3		alnex 1522	. 2 |- ( A. x -. x = y <-> -. E. x x = y )
4	2, 3	mtbir 673	1 |- -. A. x -. x = y

Syntax hints:   -. wn 3   A.wal 1371   = wceq 1373   E.wex 1515

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1470  ax-gen 1472  ax-ie2 1517  ax-i9 1553

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379

This theorem is referenced by:  equidqe  1555