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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 1434 and nfab 2182 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 2709 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 2709 | . . . 4 | |
3 | 2 | eqcomd 2045 | . . 3 |
4 | dedhb.1 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | 1, 5 | mpbiri 157 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wceq 1243 wcel 1393 cab 2026 wnfc 2165 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 |
This theorem is referenced by: (None) |
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