Theorem rexanaliim 2636

Description: A transformation of restricted quantifiers and logical connectives. (Contributed by NM, 4-Sep-2005.) (Revised by Jim Kingdon, 18-Jan-2026.)

Assertion

Ref	Expression
rexanaliim	|- ( E. x e. A ( ph /\ -. ps ) -> -. A. x e. A ( ph -> ps ) )

Proof of Theorem rexanaliim

Step	Hyp	Ref	Expression
1		annimim 690	. . 3 |- ( ( ph /\ -. ps ) -> -. ( ph -> ps ) )
2	1	reximi 2627	. 2 |- ( E. x e. A ( ph /\ -. ps ) -> E. x e. A -. ( ph -> ps ) )
3		rexnalim 2519	. 2 |- ( E. x e. A -. ( ph -> ps ) -> -. A. x e. A ( ph -> ps ) )
4	2, 3	syl 14	1 |- ( E. x e. A ( ph /\ -. ps ) -> -. A. x e. A ( ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   A.wral 2508   E.wrex 2509

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 617  ax-in2 618  ax-5 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401  df-nf 1507  df-ral 2513  df-rex 2514

This theorem is referenced by:  umgr2edg1  16007  umgr2edgneu  16010