Theorem ralexim 2497

Description: Relationship between restricted universal and existential quantifiers. (Contributed by Jim Kingdon, 17-Aug-2018.)

Assertion

Ref	Expression
ralexim	|- ( A. x e. A ph -> -. E. x e. A -. ph )

Proof of Theorem ralexim

Step	Hyp	Ref	Expression
1		rexnalim 2494	. 2 |- ( E. x e. A -. ph -> -. A. x e. A ph )
2	1	con2i 628	1 |- ( A. x e. A ph -> -. E. x e. A -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wral 2483   E.wrex 2484

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-17 1548  ax-ial 1556

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-fal 1378  df-nf 1483  df-ral 2488  df-rex 2489

This theorem is referenced by: (None)