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Mirrors > Home > MPE Home > Th. List > en3lplem2 | Structured version Visualization version Unicode version |
Description: Lemma for en3lp 8513. (Contributed by Alan Sare, 28-Oct-2011.) |
Ref | Expression |
---|---|
en3lplem2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | en3lplem1 8511 | . . . . 5 | |
2 | en3lplem1 8511 | . . . . . . . 8 | |
3 | 2 | 3comr 1273 | . . . . . . 7 |
4 | 3 | a1d 25 | . . . . . 6 |
5 | tprot 4284 | . . . . . . . . 9 | |
6 | 5 | ineq2i 3811 | . . . . . . . 8 |
7 | 6 | neeq1i 2858 | . . . . . . 7 |
8 | 7 | bicomi 214 | . . . . . 6 |
9 | 4, 8 | syl8ib 246 | . . . . 5 |
10 | jao 534 | . . . . 5 | |
11 | 1, 9, 10 | sylsyld 61 | . . . 4 |
12 | 11 | imp 445 | . . 3 |
13 | en3lplem1 8511 | . . . . . . 7 | |
14 | 13 | 3coml 1272 | . . . . . 6 |
15 | 14 | a1d 25 | . . . . 5 |
16 | tprot 4284 | . . . . . . 7 | |
17 | 16 | ineq2i 3811 | . . . . . 6 |
18 | 17 | neeq1i 2858 | . . . . 5 |
19 | 15, 18 | syl8ib 246 | . . . 4 |
20 | 19 | imp 445 | . . 3 |
21 | idd 24 | . . . . . . 7 | |
22 | dftp2 4231 | . . . . . . . 8 | |
23 | 22 | eleq2i 2693 | . . . . . . 7 |
24 | 21, 23 | syl6ib 241 | . . . . . 6 |
25 | abid 2610 | . . . . . 6 | |
26 | 24, 25 | syl6ib 241 | . . . . 5 |
27 | df-3or 1038 | . . . . 5 | |
28 | 26, 27 | syl6ib 241 | . . . 4 |
29 | 28 | imp 445 | . . 3 |
30 | 12, 20, 29 | mpjaod 396 | . 2 |
31 | 30 | ex 450 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 383 wa 384 w3o 1036 w3a 1037 wceq 1483 wcel 1990 cab 2608 wne 2794 cin 3573 c0 3915 ctp 4181 |
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-3or 1038 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-ne 2795 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-nul 3916 df-sn 4178 df-pr 4180 df-tp 4182 |
This theorem is referenced by: en3lp 8513 |
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