Theorem r19.32v 1297

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(s):   ph,x

Proof of Theorem r19.32v

Step	Hyp	Ref	Expression
1		r19.21v 1260	. 2 |- (A.x e. A (-. ph -> ps) <-> (-. ph -> A.x e. A ps))
2		df-or 197	. . 3 |- ((ph \/ ps) <-> (-. ph -> ps))
3	2	biral 1223	. 2 |- (A.x e. A (ph \/ ps) <-> A.x e. A (-. ph -> ps))
4		df-or 197	. 2 |- ((ph \/ A.x e. A ps) <-> (-. ph -> A.x e. A ps))
5	1, 3, 4	3bitr4 158	1 |- (A.x e. A (ph \/ ps) <-> (ph \/ A.x e. A ps))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   \/ wo 195  A.wral 1201

This theorem is referenced by:  iinun2 2031  iinuni 2036

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ral 1205

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