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Theorem stdpc4 2148
 Description: The specialization axiom of standard predicate calculus. It states that if a statement holds for all , then it also holds for the specific case of (properly) substituted for . Translated to traditional notation, it can be read: " , provided that is free for in ." Axiom 4 of [Mendelson] p. 69. See also spsbc 3313 and rspsbc 3379. (Contributed by NM, 14-May-1993.)
Assertion
Ref Expression
stdpc4

Proof of Theorem stdpc4
StepHypRef Expression
1 ala1 1706 . 2
2 sb2 2147 . 2
31, 2syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1436  wsb 1787 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-12 1906  ax-13 2054 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1661  df-sb 1788 This theorem is referenced by:  2stdpc4  2149  sbft  2174  spsbim  2189  spsbbi  2197  sbt  2214  sbtrt  2215  pm13.183  3213  spsbc  3313  nd1  9014  nd2  9015  bj-vexwt  31427  axfrege58b  36360  pm10.14  36572  pm11.57  36603
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