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Mirrors > Home > ILE Home > Th. List > ra5 | Unicode version |
Description: Restricted quantifier version of Axiom 5 of [Mendelson] p. 69. This is an axiom of a predicate calculus for a restricted domain. Compare the unrestricted stdpc5 1516. (Contributed by NM, 16-Jan-2004.) |
Ref | Expression |
---|---|
ra5.1 |
Ref | Expression |
---|---|
ra5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2353 | . . . 4 | |
2 | bi2.04 246 | . . . . 5 | |
3 | 2 | albii 1399 | . . . 4 |
4 | 1, 3 | bitri 182 | . . 3 |
5 | ra5.1 | . . . 4 | |
6 | 5 | stdpc5 1516 | . . 3 |
7 | 4, 6 | sylbi 119 | . 2 |
8 | df-ral 2353 | . 2 | |
9 | 7, 8 | syl6ibr 160 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1282 wnf 1389 wcel 1433 wral 2348 |
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-4 1440 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-ral 2353 |
This theorem is referenced by: (None) |
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