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Mirrors > Home > ILE Home > Th. List > dedhb | Unicode version |
Description: A deduction theorem for converting the inference => into a closed theorem. Use nfa1 1521 and nfab 2284 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 2847 is useful. (Contributed by NM, 8-Dec-2006.) |
Ref | Expression |
---|---|
dedhb.1 | |
dedhb.2 |
Ref | Expression |
---|---|
dedhb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedhb.2 | . 2 | |
2 | abidnf 2847 | . . . 4 | |
3 | 2 | eqcomd 2143 | . . 3 |
4 | dedhb.1 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | 1, 5 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 cab 2123 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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 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-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 |
This theorem is referenced by: (None) |
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