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Mirrors > Home > NFE Home > Th. List > sbciegft | Unicode version |
Description: Conversion of implicit substitution to explicit class substitution, using a bound-variable hypothesis instead of distinct variables. (Closed theorem version of sbciegf 3077.) (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
sbciegft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc5 3070 | . . 3 | |
2 | bi1 178 | . . . . . . . 8 | |
3 | 2 | imim2i 13 | . . . . . . 7 |
4 | 3 | imp3a 420 | . . . . . 6 |
5 | 4 | alimi 1559 | . . . . 5 |
6 | 19.23t 1800 | . . . . . 6 | |
7 | 6 | biimpa 470 | . . . . 5 |
8 | 5, 7 | sylan2 460 | . . . 4 |
9 | 8 | 3adant1 973 | . . 3 |
10 | 1, 9 | syl5bi 208 | . 2 |
11 | bi2 189 | . . . . . . . 8 | |
12 | 11 | imim2i 13 | . . . . . . 7 |
13 | 12 | com23 72 | . . . . . 6 |
14 | 13 | alimi 1559 | . . . . 5 |
15 | 19.21t 1795 | . . . . . 6 | |
16 | 15 | biimpa 470 | . . . . 5 |
17 | 14, 16 | sylan2 460 | . . . 4 |
18 | 17 | 3adant1 973 | . . 3 |
19 | sbc6g 3071 | . . . 4 | |
20 | 19 | 3ad2ant1 976 | . . 3 |
21 | 18, 20 | sylibrd 225 | . 2 |
22 | 10, 21 | impbid 183 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 w3a 934 wal 1540 wex 1541 wnf 1544 wceq 1642 wcel 1710 wsbc 3046 |
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-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-sbc 3047 |
This theorem is referenced by: sbciegf 3077 sbciedf 3081 |
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