Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ra4sbc Unicode version

Theorem ra4sbc 3044
 Description: Restricted quantifier version of Axiom 4 of [Mendelson] p. 69. This provides an axiom for a predicate calculus for a restricted domain. This theorem generalizes the unrestricted stdpc4 1897 and a4sbc 2978. See also ra4sbca 3045 and ra4csbela 3115. (Contributed by NM, 17-Nov-2006.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
ra4sbc
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ra4sbc
StepHypRef Expression
1 cbvralsv 2750 . 2
2 dfsbcq2 2969 . . 3
32rcla4v 2855 . 2
41, 3syl5bi 210 1
 Colors of variables: wff set class Syntax hints:   wi 6   wcel 1621  wsb 1883  wral 2518  wsbc 2966 This theorem is referenced by:  ra4sbca  3045  sbcth2  3049  ra4csbela  3115  riota5f  6297  riotass2  6300  fzrevral  10833  ra4sbc2  27433  truniALT  27441  ra4sbc2VD  27764  truniALTVD  27787  trintALTVD  27789  trintALT  27790 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ral 2523  df-v 2765  df-sbc 2967
 Copyright terms: Public domain W3C validator