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Theorem rzal 3312
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 3224 . . . 4  =/=  (/)
21necon2bi 2254 . . 3  (/)
32pm2.21d 549 . 2  (/)
43ralrimiv 2385 1  (/)
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390  wral 2300   (/)c0 3218
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-ral 2305  df-v 2553  df-dif 2914  df-nul 3219
This theorem is referenced by:  ralf0  3318
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