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Mirrors > Home > ILE Home > Th. List > fss | Unicode version |
Description: Expanding the codomain of a mapping. (Contributed by NM, 10-May-1998.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) |
Ref | Expression |
---|---|
fss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstr2 3162 |
. . . . 5
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2 | 1 | com12 30 |
. . . 4
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3 | 2 | anim2d 337 |
. . 3
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4 | df-f 5216 |
. . 3
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5 | df-f 5216 |
. . 3
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6 | 3, 4, 5 | 3imtr4g 205 |
. 2
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7 | 6 | impcom 125 |
1
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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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 df-f 5216 |
This theorem is referenced by: fssd 5374 fconst6g 5410 f1ss 5423 ffoss 5489 fsn2 5686 ofco 6095 tposf2 6263 issmo2 6284 smoiso 6297 mapsn 6684 ssdomg 6772 omp1eomlem 7087 1fv 10122 fxnn0nninf 10421 abscn2 11304 recn2 11306 imcn2 11307 climabs 11309 climre 11311 climim 11312 fsumre 11461 fsumim 11462 ismet2 13514 dvfre 13834 dvrecap 13837 lgsfcl 14069 |
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