![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > csbie | 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 2332 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | csbie.2 | . 2 ⊢ (𝑥 = 𝐴 → 𝐵 = 𝐶) | |
4 | 1, 2, 3 | csbief 3116 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶 |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1364 ∈ wcel 2160 Vcvv 2752 ⦋csb 3072 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-sbc 2978 df-csb 3073 |
This theorem is referenced by: fsumcnv 11476 fisum0diag2 11486 fprodcnv 11664 |
Copyright terms: Public domain | W3C validator |