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Theorem r19.32vr 2452
 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 2453. (Contributed by Jim Kingdon, 19-Aug-2018.)
Assertion
Ref Expression
r19.32vr ((φ x A ψ) → x A (φ ψ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.32vr
StepHypRef Expression
1 nfv 1418 . 2 xφ
21r19.32r 2451 1 ((φ x A ψ) → x A (φ ψ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∨ wo 628  ∀wral 2300 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305 This theorem is referenced by:  iinuniss  3728
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