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Theorem quantriv 24200
Description: Any wff can be trivially quantified, so long as the quantifier's set is distinct from said wff.

See also 19.9v 2011. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion
Ref Expression
quantriv  |-  ( A. x ph  <->  ph )
Distinct variable group:    ph, x

Proof of Theorem quantriv
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ x ph
2119.3 1760 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   A.wal 1532
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-nf 1540
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