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Theorem r19.21v 2374
Description: Theorem 19.21 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.21v (x A (φψ) ↔ (φx A ψ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.21v
StepHypRef Expression
1 nfv 1402 . 2 xφ
21r19.21 2373 1 (x A (φψ) ↔ (φx A ψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wral 2284
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-5 1316  ax-gen 1318  ax-4 1381  ax-17 1400  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-ral 2289
This theorem is referenced by:  r19.32vdc  2437  rmo4  2711  rmo3  2826  dftr5  3831  reusv3  4142  tfrlem1  5845  tfrlemi1  5867  tfri3  5875  rdgon  5893
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