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Theorem r19.27z 3649
Description: Restricted quantifier version of Theorem 19.27 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
r19.27z.1  F/
Assertion
Ref Expression
r19.27z
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.27z
StepHypRef Expression
1 r19.27z.1 . . . 4  F/
21r19.3rz 3642 . . 3
32anbi2d 684 . 2
4 r19.26 2747 . 2
53, 4syl6rbbr 255 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358   F/wnf 1544   wne 2517  wral 2615  c0 3551
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 2479  df-ne 2519  df-ral 2620  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-dif 3216  df-nul 3552
This theorem is referenced by:  raaan  3658
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