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Theorem r19.32vr 2503
Description: One direction of Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers. For decidable propositions this is an equivalence, as seen at r19.32vdc 2504. (Contributed by Jim Kingdon, 19-Aug-2018.)
Assertion
Ref Expression
r19.32vr  |-  ( (
ph  \/  A. x  e.  A  ps )  ->  A. x  e.  A  ( ph  \/  ps )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem r19.32vr
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
21r19.32r 2502 1  |-  ( (
ph  \/  A. x  e.  A  ps )  ->  A. x  e.  A  ( ph  \/  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 662   A.wral 2349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-ral 2354
This theorem is referenced by:  iinuniss  3766
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