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Mirrors > Home > ILE Home > Th. List > tfri1dALT | Unicode version |
Description: Alternate proof of tfri1d 6349 in terms of tfr1on 6364.
Although this does show that the tfr1on 6364 proof is general enough to
also prove tfri1d 6349, the tfri1d 6349 proof is simpler in places because it
does not need to deal with |
Ref | Expression |
---|---|
tfri1dALT.1 |
![]() ![]() ![]() ![]() ![]() ![]() |
tfri1dALT.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
tfri1dALT |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrfun 6334 |
. . . 4
![]() ![]() ![]() ![]() ![]() | |
2 | tfri1dALT.1 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | funeqi 5249 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1, 3 | mpbir 146 |
. . 3
![]() ![]() ![]() |
5 | 4 | a1i 9 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | eqid 2187 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | tfrlem8 6332 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
8 | 2 | dmeqi 4840 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | ordeq 4384 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | ax-mp 5 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 7, 10 | mpbir 146 |
. . . 4
![]() ![]() ![]() ![]() |
12 | ordsson 4503 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 11, 12 | mp1i 10 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | tfri1dALT.2 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | simpl 109 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 15 | alimi 1465 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 14, 16 | syl 14 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 17 | 19.21bi 1568 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 18 | adantr 276 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | ordon 4497 |
. . . . . . . 8
![]() ![]() ![]() | |
21 | 20 | a1i 9 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | simpr 110 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 22 | alimi 1465 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | fveq2 5527 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 24 | eleq1d 2256 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 25 | spv 1870 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 14, 23, 26 | 3syl 17 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 27 | adantr 276 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | 28 | 3ad2ant1 1019 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | onsuc 4512 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
31 | unon 4522 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() | |
32 | 30, 31 | eleq2s 2282 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 32 | adantl 277 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | onsuc 4512 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
35 | 34 | adantl 277 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
36 | 2, 19, 21, 29, 33, 35 | tfr1on 6364 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | vex 2752 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
38 | 37 | sucid 4429 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() |
39 | ssel2 3162 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
40 | 36, 38, 39 | sylancl 413 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
41 | 40 | ex 115 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
42 | 41 | ssrdv 3173 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
43 | 13, 42 | eqssd 3184 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
44 | df-fn 5231 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
45 | 5, 43, 44 | sylanbrc 417 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-coll 4130 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-setind 4548 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-ral 2470 df-rex 2471 df-reu 2472 df-rab 2474 df-v 2751 df-sbc 2975 df-csb 3070 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-iun 3900 df-br 4016 df-opab 4077 df-mpt 4078 df-tr 4114 df-id 4305 df-iord 4378 df-on 4380 df-suc 4383 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-rn 4649 df-res 4650 df-ima 4651 df-iota 5190 df-fun 5230 df-fn 5231 df-f 5232 df-f1 5233 df-fo 5234 df-f1o 5235 df-fv 5236 df-recs 6319 |
This theorem is referenced by: (None) |
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