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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj130 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj151 30947. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj130.1 | |
bnj130.2 | |
bnj130.3 | |
bnj130.4 |
Ref | Expression |
---|---|
bnj130 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj130.1 | . . 3 | |
2 | 1 | sbcbii 3491 | . 2 |
3 | bnj130.4 | . 2 | |
4 | bnj105 30790 | . . . . . . . . . 10 | |
5 | 4 | bnj90 30788 | . . . . . . . . 9 |
6 | 5 | bicomi 214 | . . . . . . . 8 |
7 | bnj130.2 | . . . . . . . 8 | |
8 | bnj130.3 | . . . . . . . 8 | |
9 | 6, 7, 8 | 3anbi123i 1251 | . . . . . . 7 |
10 | sbc3an 3494 | . . . . . . 7 | |
11 | 9, 10 | bitr4i 267 | . . . . . 6 |
12 | 11 | eubii 2492 | . . . . 5 |
13 | 4 | bnj89 30787 | . . . . 5 |
14 | 12, 13 | bitr4i 267 | . . . 4 |
15 | 14 | imbi2i 326 | . . 3 |
16 | nfv 1843 | . . . . 5 | |
17 | 16 | sbc19.21g 3502 | . . . 4 |
18 | 4, 17 | ax-mp 5 | . . 3 |
19 | 15, 18 | bitr4i 267 | . 2 |
20 | 2, 3, 19 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wcel 1990 weu 2470 cvv 3200 wsbc 3435 wfn 5883 c1o 7553 w-bnj15 30758 |
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 ax-sep 4781 ax-nul 4789 ax-pow 4843 |
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-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-pw 4160 df-sn 4178 df-suc 5729 df-fn 5891 df-1o 7560 |
This theorem is referenced by: bnj151 30947 |
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