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Theorem r19.27m 3344
 Description: Restricted quantifier version of Theorem 19.27 of [Margaris] p. 90. It is valid only when the domain of quantification is inhabited. (Contributed by Jim Kingdon, 5-Aug-2018.)
Hypothesis
Ref Expression
r19.27m.1
Assertion
Ref Expression
r19.27m
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.27m
StepHypRef Expression
1 r19.27m.1 . . . 4
21r19.3rm 3338 . . 3
32anbi2d 445 . 2
4 r19.26 2458 . 2
53, 4syl6rbbr 192 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wnf 1365  wex 1397   wcel 1409  wral 2323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-cleq 2049  df-clel 2052  df-ral 2328 This theorem is referenced by:  r19.27mv  3345  raaanlem  3354
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