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Mirrors > Home > ILE Home > Th. List > eqerlem | Unicode version |
Description: Lemma for eqer 6429. (Contributed by NM, 17-Mar-2008.) (Proof shortened by Mario Carneiro, 6-Dec-2016.) |
Ref | Expression |
---|---|
eqer.1 | |
eqer.2 |
Ref | Expression |
---|---|
eqerlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqer.2 | . . 3 | |
2 | 1 | brabsb 4153 | . 2 |
3 | vex 2663 | . . 3 | |
4 | nfcsb1v 3005 | . . . . 5 | |
5 | nfcsb1v 3005 | . . . . 5 | |
6 | 4, 5 | nfeq 2266 | . . . 4 |
7 | vex 2663 | . . . . . 6 | |
8 | nfv 1493 | . . . . . . 7 | |
9 | vex 2663 | . . . . . . . . . 10 | |
10 | nfcv 2258 | . . . . . . . . . 10 | |
11 | eqer.1 | . . . . . . . . . 10 | |
12 | 9, 10, 11 | csbief 3014 | . . . . . . . . 9 |
13 | csbeq1 2978 | . . . . . . . . 9 | |
14 | 12, 13 | syl5eqr 2164 | . . . . . . . 8 |
15 | 14 | eqeq2d 2129 | . . . . . . 7 |
16 | 8, 15 | sbciegf 2912 | . . . . . 6 |
17 | 7, 16 | ax-mp 5 | . . . . 5 |
18 | csbeq1a 2983 | . . . . . 6 | |
19 | 18 | eqeq1d 2126 | . . . . 5 |
20 | 17, 19 | syl5bb 191 | . . . 4 |
21 | 6, 20 | sbciegf 2912 | . . 3 |
22 | 3, 21 | ax-mp 5 | . 2 |
23 | 2, 22 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wcel 1465 cvv 2660 wsbc 2882 csb 2975 class class class wbr 3899 copab 3958 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 |
This theorem is referenced by: eqer 6429 |
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