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Mirrors > Home > ILE Home > Th. List > csbconstg | GIF version |
Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 2857 with distinct variable requirement. (Contributed by Alan Sare, 22-Jul-2012.) |
Ref | Expression |
---|---|
csbconstg | ⊢ (A ∈ 𝑉 → ⦋A / x⦌B = B) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2175 | . 2 ⊢ ℲxB | |
2 | 1 | csbconstgf 2857 | 1 ⊢ (A ∈ 𝑉 → ⦋A / x⦌B = B) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1242 ∈ wcel 1390 ⦋csb 2846 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-sbc 2759 df-csb 2847 |
This theorem is referenced by: sbcel1g 2863 sbceq1g 2864 sbcel2g 2865 sbceq2g 2866 csbidmg 2896 sbcbr12g 3805 sbcbr1g 3806 sbcbr2g 3807 sbcrel 4369 csbcnvg 4462 csbresg 4558 sbcfung 4868 csbfv12g 5152 csbfv2g 5153 csbov12g 5486 csbov1g 5487 csbov2g 5488 |
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