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Theorem ral0 3316
Description: Vacuous universal quantification is always true. (Contributed by NM, 20-Oct-2005.)
Assertion
Ref Expression
ral0 x φ

Proof of Theorem ral0
StepHypRef Expression
1 noel 3222 . . 3 ¬ x
21pm2.21i 574 . 2 (x ∅ → φ)
32rgen 2368 1 x φ
Colors of variables: wff set class
Syntax hints:   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-ral 2305  df-v 2553  df-dif 2914  df-nul 3219
This theorem is referenced by:  0iin  3706  po0  4039  so0  4054  ord0  4094  mpt0  4969  bj-nntrans  9385
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