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Mirrors > Home > MPE Home > Th. List > ffnov | Structured version Visualization version Unicode version |
Description: An operation maps to a class to which all values belong. (Contributed by NM, 7-Feb-2004.) |
Ref | Expression |
---|---|
ffnov |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffnfv 6049 |
. 2
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2 | fveq2 5865 |
. . . . . 6
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3 | df-ov 6293 |
. . . . . 6
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4 | 2, 3 | syl6eqr 2503 |
. . . . 5
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5 | 4 | eleq1d 2513 |
. . . 4
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6 | 5 | ralxp 4976 |
. . 3
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7 | 6 | anbi2i 700 |
. 2
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8 | 1, 7 | bitri 253 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-iun 4280 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-fv 5590 df-ov 6293 |
This theorem is referenced by: fovcl 6401 cantnfvalf 8170 axaddf 9569 axmulf 9570 mulnzcnopr 10258 frmdplusg 16638 gass 16955 sylow2blem2 17273 matecl 19450 txdis1cn 20650 isxmet2d 21342 prdsmet 21385 imasdsf1olem 21388 imasf1oxmet 21390 imasf1omet 21391 xmetresbl 21452 comet 21528 tgqioo 21818 xrtgioo 21824 opnmblALT 22561 dvdsmulf1o 24123 issubgoi 26038 ghgrpOLD 26096 fovcld 28239 pstmxmet 28700 xrge0pluscn 28746 isbndx 32114 isbnd3 32116 isbnd3b 32117 prdsbnd 32125 isdrngo2 32197 clintopcllaw 39900 |
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