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Theorem r19.28z 3642
 Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. It is valid only when the domain of quantification is not empty. (Contributed by NM, 26-Oct-2010.)
Hypothesis
Ref Expression
r19.3rz.1
Assertion
Ref Expression
r19.28z
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.28z
StepHypRef Expression
1 r19.3rz.1 . . . 4
21r19.3rz 3641 . . 3
32anbi1d 685 . 2
4 r19.26 2746 . 2
53, 4syl6rbbr 255 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wnf 1544   wne 2516  wral 2614  c0 3550 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551 This theorem is referenced by:  raaan  3657
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