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Theorem ralf0 3936
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:   ,

Proof of Theorem ralf0
StepHypRef Expression
1 ralf0.1 . . . . 5
2 con3 134 . . . . 5
31, 2mpi 17 . . . 4
43alimi 1633 . . 3
5 df-ral 2812 . . 3
6 eq0 3800 . . 3
74, 5, 63imtr4i 266 . 2
8 rzal 3931 . 2
97, 8impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  A.wral 2807   c0 3784
This theorem is referenced by:  uvtx01vtx  24492  rusgra0edg  24955
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-nul 3785
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