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Mirrors > Home > NFE 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. See also spsbc 3058 and rspsbc 3124. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
stdpc4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . . 3 | |
2 | 1 | alimi 1559 | . 2 |
3 | sb2 2023 | . 2 | |
4 | 2, 3 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wal 1540 wsb 1648 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 |
This theorem is referenced by: sbft 2025 spsbe 2075 spsbim 2076 spsbbi 2077 sb8 2092 sb9i 2094 pm13.183 2979 spsbc 3058 |
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