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Theorem 19.25 1721
Description: Theorem 19.25 of [Margaris] p. 90.
Assertion
Ref Expression
19.25 |- (A.yE.x(ph -> ps) -> (E.yA.xph -> E.yE.xps))

Proof of Theorem 19.25
StepHypRef Expression
1 19.35 1712 . . . 4 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
21biimpi 224 . . 3 |- (E.x(ph -> ps) -> (A.xph -> E.xps))
32alimi 1627 . 2 |- (A.yE.x(ph -> ps) -> A.y(A.xph -> E.xps))
4 exim 1675 . 2 |- (A.y(A.xph -> E.xps) -> (E.yA.xph -> E.yE.xps))
53, 4syl 13 1 |- (A.yE.x(ph -> ps) -> (E.yA.xph -> E.yE.xps))
Colors of variables: wff set class
Syntax hints:   -> wi 3  A.wal 1584  E.wex 1615
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1593  ax-4 1608  ax-5o 1610
This theorem depends on definitions:  df-bi 220  df-an 339  df-ex 1616
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