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Mirrors > Home > ILE Home > Th. List > ovelrn | Unicode version |
Description: A member of an operation's range is a value of the operation. (Contributed by NM, 7-Feb-2007.) (Revised by Mario Carneiro, 30-Jan-2014.) |
Ref | Expression |
---|---|
ovelrn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnrnov 5978 | . . 3 | |
2 | 1 | eleq2d 2234 | . 2 |
3 | elex 2732 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | fnovex 5866 | . . . . . 6 | |
6 | eleq1 2227 | . . . . . 6 | |
7 | 5, 6 | syl5ibrcom 156 | . . . . 5 |
8 | 7 | 3expb 1193 | . . . 4 |
9 | 8 | rexlimdvva 2589 | . . 3 |
10 | eqeq1 2171 | . . . . . 6 | |
11 | 10 | 2rexbidv 2489 | . . . . 5 |
12 | 11 | elabg 2867 | . . . 4 |
13 | 12 | a1i 9 | . . 3 |
14 | 4, 9, 13 | pm5.21ndd 695 | . 2 |
15 | 2, 14 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 967 wceq 1342 wcel 2135 cab 2150 wrex 2443 cvv 2721 cxp 4596 crn 4599 wfn 5177 (class class class)co 5836 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-iota 5147 df-fun 5184 df-fn 5185 df-fv 5190 df-ov 5839 |
This theorem is referenced by: blrnps 12958 blrn 12959 tgioo 13093 |
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