Theorem ralinexa 1686

Description: A transformation of restricted quantifiers and logical connectives.

Assertion

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

Proof of Theorem ralinexa

Step	Hyp	Ref	Expression
1		imnan 242	. . 3 |- ((ph -> -. ps) <-> -. (ph /\ ps))
2	1	ralbii 1670	. 2 |- (A.x e. A (ph -> -. ps) <-> A.x e. A -. (ph /\ ps))
3		ralnex 1656	. 2 |- (A.x e. A -. (ph /\ ps) <-> -. E.x e. A (ph /\ ps))
4	2, 3	bitr 173	1 |- (A.x e. A (ph -> -. ps) <-> -. E.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:  kmlem7 4781  kmlem13 4787  sncld 7784

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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