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Mirrors > Home > MPE Home > Th. List > fvexi | Structured version Visualization version GIF version |
Description: The value of a class exists. Inference form of fvex 6201. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
fvexi.1 | ⊢ 𝐴 = (𝐹‘𝐵) |
Ref | Expression |
---|---|
fvexi | ⊢ 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvexi.1 | . 2 ⊢ 𝐴 = (𝐹‘𝐵) | |
2 | fvex 6201 | . 2 ⊢ (𝐹‘𝐵) ∈ V | |
3 | 1, 2 | eqeltri 2697 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∈ wcel 1990 Vcvv 3200 ‘cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 df-fv 5896 |
This theorem is referenced by: rmodislmod 18931 setsvtx 25927 usgredgffibi 26216 vtxdginducedm1lem1 26435 vtxdginducedm1lem4 26438 vtxdginducedm1 26439 vtxdginducedm1fi 26440 finsumvtxdg2ssteplem4 26444 frgrwopreg1 27182 eulerpartlemgvv 30438 limsupequzmpt2 39950 climuzlem 39975 climisp 39978 climxrrelem 39981 climxrre 39982 limsupgtlem 40009 liminflelimsupuz 40017 liminfgelimsupuz 40020 liminfequzmpt2 40023 liminfvaluz 40024 limsupvaluz3 40030 climliminflimsupd 40033 liminfreuzlem 40034 liminfltlem 40036 liminflimsupclim 40039 xlimclim2lem 40065 climxlim2 40072 smflimmpt 41016 smflimsuplem4 41029 smflimsuplem6 41031 smflimsuplem8 41033 smfliminflem 41036 isupwlkg 41718 |
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