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Mirrors > Home > ILE Home > Th. List > stdpc4 | Unicode version |
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.) |
Ref | Expression |
---|---|
stdpc4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . . 3 | |
2 | 1 | alimi 1442 | . 2 |
3 | sb2 1754 | . 2 | |
4 | 2, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1340 wsb 1749 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-i9 1517 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-sb 1750 |
This theorem is referenced by: sbh 1763 sbft 1835 pm13.183 2859 spsbc 2957 |
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