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Theorem quantriv 24247
Description: Any wff can be trivially quantified, so long as the quantifier's set is distinct from said wff.

See also 19.9v 1664. (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 1606 . 2  |-  F/ x ph
2119.3 1783 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   A.wal 1528
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-nf 1533
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