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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 2982 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 2255 | . 2 ⊢ Ⅎ𝑥𝐵 | |
2 | 1 | csbconstgf 2982 | 1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1314 ∈ wcel 1463 ⦋csb 2971 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-sbc 2879 df-csb 2972 |
This theorem is referenced by: sbcel1g 2988 sbceq1g 2989 sbcel2g 2990 sbceq2g 2991 csbidmg 3022 sbcbr12g 3945 sbcbr1g 3946 sbcbr2g 3947 sbcrel 4585 csbcnvg 4683 csbresg 4780 sbcfung 5105 csbfv12g 5411 csbfv2g 5412 elfvmptrab 5470 csbov12g 5764 csbov1g 5765 csbov2g 5766 |
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