Theorem r19.32v 1755

Description: Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers.

Assertion

Ref	Expression
r19.32v	|- (A.x e. A (ph \/ ps) <-> (ph \/ A.x e. A ps))

Distinct variable group:   ph,x

Proof of Theorem r19.32v

Step	Hyp	Ref	Expression
1		r19.21v 1713	. 2 |- (A.x e. A (-. ph -> ps) <-> (-. ph -> A.x e. A ps))
2		df-or 224	. . 3 |- ((ph \/ ps) <-> (-. ph -> ps))
3	2	ralbii 1664	. 2 |- (A.x e. A (ph \/ ps) <-> A.x e. A (-. ph -> ps))
4		df-or 224	. 2 |- ((ph \/ A.x e. A ps) <-> (-. ph -> A.x e. A ps))
5	1, 3, 4	3bitr4 183	1 |- (A.x e. A (ph \/ ps) <-> (ph \/ A.x e. A ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222  A.wral 1642

This theorem is referenced by:  iinun2 2604  iinuni 2610

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ral 1646

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