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Mirrors > Home > NFE Home > Th. List > eqsbc3r | Unicode version |
Description: eqsbc3 3085 with setvar variable on right side of equals sign. This proof was automatically generated from the virtual deduction proof eqsbc3rVD in set.mm using a translation program. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
eqsbc3r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2355 | . . . . . 6 | |
2 | 1 | sbcbii 3101 | . . . . 5 |
3 | 2 | biimpi 186 | . . . 4 |
4 | eqsbc3 3085 | . . . 4 | |
5 | 3, 4 | syl5ib 210 | . . 3 |
6 | eqcom 2355 | . . 3 | |
7 | 5, 6 | syl6ib 217 | . 2 |
8 | idd 21 | . . . . 5 | |
9 | 8, 6 | syl6ibr 218 | . . . 4 |
10 | 9, 4 | sylibrd 225 | . . 3 |
11 | 10, 2 | syl6ibr 218 | . 2 |
12 | 7, 11 | impbid 183 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wcel 1710 wsbc 3046 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-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: (None) |
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