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Theorem r19.2z 3639
 Description: Theorem 19.2 of [Margaris] p. 89 with restricted quantifiers (compare 19.2 1659). The restricted version is valid only when the domain of quantification is not empty. (Contributed by NM, 15-Nov-2003.)
Assertion
Ref Expression
r19.2z
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem r19.2z
StepHypRef Expression
1 df-ral 2619 . . . 4
2 exintr 1614 . . . 4
31, 2sylbi 187 . . 3
4 n0 3559 . . 3
5 df-rex 2620 . . 3
63, 4, 53imtr4g 261 . 2
76impcom 419 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wal 1540  wex 1541   wcel 1710   wne 2516  wral 2614  wrex 2615  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-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551 This theorem is referenced by:  r19.2zb  3640  intssuni  3948  riinn0  4040
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