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Mirrors > Home > ILE Home > Th. List > abrexex2 | Unicode version |
Description: Existence of an existentially restricted class abstraction. is normally has free-variable parameters and . See also abrexex 5983. (Contributed by NM, 12-Sep-2004.) |
Ref | Expression |
---|---|
abrexex2.1 | |
abrexex2.2 |
Ref | Expression |
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abrexex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . . . 4 | |
2 | nfcv 2258 | . . . . 5 | |
3 | nfs1v 1892 | . . . . 5 | |
4 | 2, 3 | nfrexxy 2449 | . . . 4 |
5 | sbequ12 1729 | . . . . 5 | |
6 | 5 | rexbidv 2415 | . . . 4 |
7 | 1, 4, 6 | cbvab 2240 | . . 3 |
8 | df-clab 2104 | . . . . 5 | |
9 | 8 | rexbii 2419 | . . . 4 |
10 | 9 | abbii 2233 | . . 3 |
11 | 7, 10 | eqtr4i 2141 | . 2 |
12 | df-iun 3785 | . . 3 | |
13 | abrexex2.1 | . . . 4 | |
14 | abrexex2.2 | . . . 4 | |
15 | 13, 14 | iunex 5989 | . . 3 |
16 | 12, 15 | eqeltrri 2191 | . 2 |
17 | 11, 16 | eqeltri 2190 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 wsb 1720 cab 2103 wrex 2394 cvv 2660 ciun 3783 |
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-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-coll 4013 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
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-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 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-uni 3707 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 |
This theorem is referenced by: abexssex 5991 abexex 5992 oprabrexex2 5996 ab2rexex 5997 ab2rexex2 5998 |
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