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Theorem ralf0 3878
 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 140 . . . . 5
31, 2mpi 20 . . . 4
43alimi 1686 . . 3
5 df-ral 2744 . . 3
6 eq0 3749 . . 3
74, 5, 63imtr4i 270 . 2
8 rzal 3873 . 2
97, 8impbii 191 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188  wal 1444   wceq 1446   wcel 1889  wral 2739  c0 3733 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-ral 2744  df-v 3049  df-dif 3409  df-nul 3734 This theorem is referenced by:  uvtx01vtx  25232  rusgra0edg  25695
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