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Mirrors > Home > NFE Home > Th. List > rnex | GIF version |
Description: The range of a set is a set. Corollary 6.8(3) of [TakeutiZaring] p. 26. Similar to Lemma 3D of [Enderton] p. 41. (Contributed by set.mm contributors, 7-Jul-2008.) |
Ref | Expression |
---|---|
dmex.1 | ⊢ A ∈ V |
Ref | Expression |
---|---|
rnex | ⊢ ran A ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmex.1 | . 2 ⊢ A ∈ V | |
2 | rnexg 5104 | . 2 ⊢ (A ∈ V → ran A ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ran A ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1710 Vcvv 2859 ran crn 4773 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-addc 4378 df-nnc 4379 df-phi 4565 df-op 4566 df-br 4640 df-ima 4727 df-rn 4786 |
This theorem is referenced by: elxp4 5108 ffoss 5314 foundex 5914 mapexi 6003 bren 6030 enex 6031 enmap1lem5 6073 ovmuc 6130 mucex 6133 ovcelem1 6171 ceex 6174 sbthlem1 6203 sbthlem3 6205 tcfnex 6244 nmembers1lem1 6268 nncdiv3lem2 6276 nnc3n3p1 6278 nchoicelem11 6299 nchoicelem16 6304 nchoicelem18 6306 frecxp 6314 |
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