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Theorem ral0 3350
Description: Vacuous universal quantification is always true. (Contributed by NM, 20-Oct-2005.)
Assertion
Ref Expression
ral0  |-  A. x  e.  (/)  ph

Proof of Theorem ral0
StepHypRef Expression
1 noel 3262 . . 3  |-  -.  x  e.  (/)
21pm2.21i 608 . 2  |-  ( x  e.  (/)  ->  ph )
32rgen 2417 1  |-  A. x  e.  (/)  ph
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   A.wral 2349   (/)c0 3258
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-v 2604  df-dif 2976  df-nul 3259
This theorem is referenced by:  0iin  3744  po0  4074  so0  4089  we0  4124  ord0  4154  mpt0  5057  ac6sfi  6431  uzsinds  9518  rexfiuz  10013  fimaxre2  10247  2prm  10653  bj-nntrans  10904
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