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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 5 | . . 3 | |
2 | 1 | alimi 1384 | . 2 |
3 | sb2 1690 | . 2 | |
4 | 2, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1282 wsb 1685 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-sb 1686 |
This theorem is referenced by: sbh 1699 sbft 1769 pm13.183 2732 spsbc 2826 |
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