Theorem rexanali 1687

Description: A transformation of restricted quantifiers and logical connectives.

Assertion

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

Proof of Theorem rexanali

Step	Hyp	Ref	Expression
1		annim 238	. . 3 |- ((ph /\ -. ps) <-> -. (ph -> ps))
2	1	rexbii 1671	. 2 |- (E.x e. A (ph /\ -. ps) <-> E.x e. A -. (ph -> ps))
3		rexnal 1657	. 2 |- (E.x e. A -. (ph -> ps) <-> -. A.x e. A (ph -> ps))
4	2, 3	bitr 173	1 |- (E.x e. A (ph /\ -. ps) <-> -. A.x e. A (ph -> ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   /\ wa 223  A.wral 1648  E.wrex 1649

This theorem is referenced by:  supxrre 6085  qsqueeze 6281  climrecl 7110  climge0 7112  elcls 7701

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-ral 1652  df-rex 1653

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