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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 1528 and nfab 2311 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 2889 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 2889 | . . . 4 | |
3 | 2 | eqcomd 2170 | . . 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 1340 wceq 1342 wcel 2135 cab 2150 wnfc 2293 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 |
This theorem is referenced by: (None) |
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