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Theorem ralf0 3758
 Description: The quantification of a falsehood is vacuous when true. (Contributed by NM, 26-Nov-2005.)
Hypothesis
Ref Expression
ralf0.1
Assertion
Ref Expression
ralf0
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem ralf0
StepHypRef Expression
1 ralf0.1 . . . . 5
2 con3 129 . . . . 5
31, 2mpi 17 . . . 4
43alimi 1569 . . 3
5 df-ral 2716 . . 3
6 eq0 3627 . . 3
74, 5, 63imtr4i 259 . 2
8 rzal 3753 . 2
97, 8impbii 182 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550   wceq 1653   wcel 1727  wral 2711  c0 3613 This theorem is referenced by:  uvtx01vtx  21532 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-v 2964  df-dif 3309  df-nul 3614
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