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Mirrors > Home > MPE Home > Th. List > Mathboxes > 2sbc5g | Structured version Visualization version Unicode version |
Description: Theorem *13.22 in [WhiteheadRussell] p. 179. (Contributed by Andrew Salmon, 3-Jun-2011.) |
Ref | Expression |
---|---|
2sbc5g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2633 | . . . . . . 7 | |
2 | 1 | anbi2d 740 | . . . . . 6 |
3 | 2 | anbi1d 741 | . . . . 5 |
4 | 3 | 2exbidv 1852 | . . . 4 |
5 | dfsbcq 3437 | . . . . 5 | |
6 | 5 | sbcbidv 3490 | . . . 4 |
7 | 4, 6 | bibi12d 335 | . . 3 |
8 | eqeq2 2633 | . . . . . . 7 | |
9 | 8 | anbi1d 741 | . . . . . 6 |
10 | 9 | anbi1d 741 | . . . . 5 |
11 | 10 | 2exbidv 1852 | . . . 4 |
12 | dfsbcq 3437 | . . . 4 | |
13 | 11, 12 | bibi12d 335 | . . 3 |
14 | sbc5 3460 | . . . 4 | |
15 | 19.42v 1918 | . . . . . 6 | |
16 | anass 681 | . . . . . . 7 | |
17 | 16 | exbii 1774 | . . . . . 6 |
18 | sbc5 3460 | . . . . . . 7 | |
19 | 18 | anbi2i 730 | . . . . . 6 |
20 | 15, 17, 19 | 3bitr4ri 293 | . . . . 5 |
21 | 20 | exbii 1774 | . . . 4 |
22 | 14, 21 | bitr2i 265 | . . 3 |
23 | 7, 13, 22 | vtocl2g 3270 | . 2 |
24 | 23 | ancoms 469 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 wsbc 3435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-sbc 3436 |
This theorem is referenced by: pm14.123b 38627 |
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