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Mirrors > Home > ILE Home > Th. List > spcgf | Unicode version |
Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 2-Feb-1997.) (Revised by Andrew Salmon, 12-Aug-2011.) |
Ref | Expression |
---|---|
spcgf.1 | |
spcgf.2 | |
spcgf.3 |
Ref | Expression |
---|---|
spcgf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spcgf.2 | . . 3 | |
2 | spcgf.1 | . . 3 | |
3 | 1, 2 | spcgft 2758 | . 2 |
4 | spcgf.3 | . 2 | |
5 | 3, 4 | mpg 1427 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wnf 1436 wcel 1480 wnfc 2266 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 |
This theorem is referenced by: spcgv 2768 rspc 2778 elabgt 2820 eusvnf 4369 mpofvex 6094 |
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