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Mirrors > Home > MPE Home > Th. List > ovexi | Structured version Visualization version GIF version |
Description: The result of an operation is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
Ref | Expression |
---|---|
ovexi.1 | ⊢ 𝐴 = (𝐵𝐹𝐶) |
Ref | Expression |
---|---|
ovexi | ⊢ 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovexi.1 | . 2 ⊢ 𝐴 = (𝐵𝐹𝐶) | |
2 | ovex 6942 | . 2 ⊢ (𝐵𝐹𝐶) ∈ V | |
3 | 1, 2 | eqeltri 2902 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1656 ∈ wcel 2164 Vcvv 3414 (class class class)co 6910 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-13 2389 ax-ext 2803 ax-nul 5015 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-mo 2605 df-eu 2640 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-ral 3122 df-rex 3123 df-v 3416 df-sbc 3663 df-dif 3801 df-un 3803 df-in 3805 df-ss 3812 df-nul 4147 df-sn 4400 df-pr 4402 df-uni 4661 df-iota 6090 df-fv 6135 df-ov 6913 |
This theorem is referenced by: negex 10606 decex 11832 gsumress 17636 nghmfval 22903 2pthon3v 27279 konigsberglem5 27631 dpval 30139 cdleme31snd 36456 c0exALT 38044 subsalsal 41362 rrxline 43298 |
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