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Theorem r19.32vr 2579
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 2580. (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 1508 . 2  |-  F/ x ph
21r19.32r 2578 1  |-  ( (
ph  \/  A. x  e.  A  ps )  ->  A. x  e.  A  ( ph  \/  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 697   A.wral 2416
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-gen 1425  ax-4 1487  ax-17 1506
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2421
This theorem is referenced by:  iinuniss  3895
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