Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj976 | Structured version Visualization version Unicode version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj976.1 | |
bnj976.2 | |
bnj976.3 | |
bnj976.4 | |
bnj976.5 |
Ref | Expression |
---|---|
bnj976 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj976.4 | . 2 | |
2 | sbcco 3458 | . 2 | |
3 | bnj976.5 | . . 3 | |
4 | bnj252 30769 | . . . . . 6 | |
5 | 4 | sbcbii 3491 | . . . . 5 |
6 | bnj976.1 | . . . . . 6 | |
7 | 6 | sbcbii 3491 | . . . . 5 |
8 | vex 3203 | . . . . . . . 8 | |
9 | 8 | bnj525 30807 | . . . . . . 7 |
10 | sbc3an 3494 | . . . . . . . 8 | |
11 | bnj62 30786 | . . . . . . . . 9 | |
12 | 11 | 3anbi1i 1253 | . . . . . . . 8 |
13 | 10, 12 | bitri 264 | . . . . . . 7 |
14 | 9, 13 | anbi12i 733 | . . . . . 6 |
15 | sbcan 3478 | . . . . . 6 | |
16 | bnj252 30769 | . . . . . 6 | |
17 | 14, 15, 16 | 3bitr4ri 293 | . . . . 5 |
18 | 5, 7, 17 | 3bitr4i 292 | . . . 4 |
19 | fneq1 5979 | . . . . . . 7 | |
20 | sbceq1a 3446 | . . . . . . . 8 | |
21 | bnj976.2 | . . . . . . . . 9 | |
22 | sbcco 3458 | . . . . . . . . 9 | |
23 | 21, 22 | bitr4i 267 | . . . . . . . 8 |
24 | 20, 23 | syl6bbr 278 | . . . . . . 7 |
25 | sbceq1a 3446 | . . . . . . . 8 | |
26 | bnj976.3 | . . . . . . . . 9 | |
27 | sbcco 3458 | . . . . . . . . 9 | |
28 | 26, 27 | bitr4i 267 | . . . . . . . 8 |
29 | 25, 28 | syl6bbr 278 | . . . . . . 7 |
30 | 19, 24, 29 | 3anbi123d 1399 | . . . . . 6 |
31 | 30 | anbi2d 740 | . . . . 5 |
32 | bnj252 30769 | . . . . 5 | |
33 | 31, 16, 32 | 3bitr4g 303 | . . . 4 |
34 | 18, 33 | syl5bb 272 | . . 3 |
35 | 3, 34 | sbcie 3470 | . 2 |
36 | 1, 2, 35 | 3bitr2i 288 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 cvv 3200 wsbc 3435 wfn 5883 w-bnj17 30752 |
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-3an 1039 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-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-fun 5890 df-fn 5891 df-bnj17 30753 |
This theorem is referenced by: bnj910 31018 bnj999 31027 bnj907 31035 |
Copyright terms: Public domain | W3C validator |