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Theorem rzal 3318
 Description: Vacuous quantification is always true. (Contributed by NM, 11-Mar-1997.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
rzal
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rzal
StepHypRef Expression
1 ne0i 3230 . . . 4
21necon2bi 2260 . . 3
32pm2.21d 549 . 2
43ralrimiv 2391 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  wral 2306  c0 3224 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-ral 2311  df-v 2559  df-dif 2920  df-nul 3225 This theorem is referenced by:  ralf0  3324
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