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Mirrors > Home > ILE Home > Th. List > stdpc5 | Unicode version |
Description: An axiom scheme of standard predicate calculus that emulates Axiom 5 of [Mendelson] p. 69. The hypothesis can be thought of as emulating " is not free in ." With this definition, the meaning of "not free" is less restrictive than the usual textbook definition; for example would not (for us) be free in by nfequid 1635. This theorem scheme can be proved as a metatheorem of Mendelson's axiom system, even though it is slightly stronger than his Axiom 5. (Contributed by NM, 22-Sep-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) |
Ref | Expression |
---|---|
stdpc5.1 |
Ref | Expression |
---|---|
stdpc5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stdpc5.1 | . . 3 | |
2 | 1 | 19.21 1520 | . 2 |
3 | 2 | biimpi 118 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1287 wnf 1394 |
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 1381 ax-gen 1383 ax-4 1445 ax-ial 1472 ax-i5r 1473 |
This theorem depends on definitions: df-bi 115 df-nf 1395 |
This theorem is referenced by: sbalyz 1923 ra5 2927 |
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