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Mirrors > Home > MPE Home > Th. List > csbie | Structured version Visualization version GIF version |
Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by AV, 2-Dec-2019.) |
Ref | Expression |
---|---|
csbie.1 | ⊢ 𝐴 ∈ V |
csbie.2 | ⊢ (𝑥 = 𝐴 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
csbie | ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbie.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | nfcv 2979 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | csbie.2 | . 2 ⊢ (𝑥 = 𝐴 → 𝐵 = 𝐶) | |
4 | 1, 2, 3 | csbief 3919 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∈ wcel 2114 Vcvv 3496 ⦋csb 3885 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-v 3498 df-sbc 3775 df-csb 3886 |
This theorem is referenced by: pofun 5493 eqerlem 8325 mptnn0fsuppd 13369 fsum 15079 fsumcnv 15130 fsumshftm 15138 fsum0diag2 15140 fprod 15297 fprodcnv 15339 bpolyval 15405 ruclem1 15586 odfval 18662 odval 18664 psrass1lem 20159 selvval 20333 mamufval 20998 pm2mpval 21405 isibl 24368 dfitg 24372 dvfsumlem2 24626 fsumdvdsmul 25774 disjxpin 30340 poimirlem1 34895 poimirlem5 34899 poimirlem15 34909 poimirlem16 34910 poimirlem17 34911 poimirlem19 34913 poimirlem20 34914 poimirlem22 34916 poimirlem24 34918 poimirlem28 34922 fphpd 39420 monotuz 39545 oddcomabszz 39548 fnwe2val 39656 fnwe2lem1 39657 |
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