Theorem r19.26-2 1751

Description: Theorem 19.26 of [Margaris] p. 90 with 2 restricted quantifiers.

Assertion

Ref	Expression
r19.26-2	|- (A.x e. A A.y e. B (ph /\ ps) <-> (A.x e. A A.y e. B ph /\ A.x e. A A.y e. B ps))

Proof of Theorem r19.26-2

Step	Hyp	Ref	Expression
1		r19.26 1750	. . 3 |- (A.y e. B (ph /\ ps) <-> (A.y e. B ph /\ A.y e. B ps))
2	1	ralbii 1667	. 2 |- (A.x e. A A.y e. B (ph /\ ps) <-> A.x e. A (A.y e. B ph /\ A.y e. B ps))
3		r19.26 1750	. 2 |- (A.x e. A (A.y e. B ph /\ A.y e. B ps) <-> (A.x e. A A.y e. B ph /\ A.x e. A A.y e. B ps))
4	2, 3	bitr 173	1 |- (A.x e. A A.y e. B (ph /\ ps) <-> (A.x e. A A.y e. B ph /\ A.x e. A A.y e. B ps))

Syntax hints:   <-> wb 146   /\ wa 223  A.wral 1645

This theorem is referenced by:  fununi 3563  tz7.48lem 3955  ajmoi 8519  adjmo 9758

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ral 1649

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