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Theorem stdpc4 1655
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. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
stdpc4

Proof of Theorem stdpc4
StepHypRef Expression
1 ax-1 5 . . 3
21alimi 1341 . 2
3 sb2 1647 . 2
42, 3syl 14 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240  wsb 1642
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  sbh  1656  sbft  1725  pm13.183  2675  spsbc  2769
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