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Mirrors > Home > NFE Home > Th. List > dedhb | Unicode version |
Description: A deduction theorem for converting the inference => into a closed theorem. Use nfa1 1788 and nfab 2493 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 3005 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 3005 | . . . 4 | |
3 | 2 | eqcomd 2358 | . . 3 |
4 | dedhb.1 | . . 3 | |
5 | 3, 4 | syl 15 | . 2 |
6 | 1, 5 | mpbiri 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wal 1540 wceq 1642 wcel 1710 cab 2339 wnfc 2476 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 |
This theorem is referenced by: (None) |
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