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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 3053 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 2306 | . 2 ⊢ Ⅎ𝑥𝐵 | |
2 | 1 | csbconstgf 3053 | 1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1342 ∈ wcel 2135 ⦋csb 3040 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-sbc 2947 df-csb 3041 |
This theorem is referenced by: sbcel1g 3059 sbceq1g 3060 sbcel2g 3061 sbceq2g 3062 csbidmg 3096 sbcbr12g 4031 sbcbr1g 4032 sbcbr2g 4033 sbcrel 4684 csbcnvg 4782 csbresg 4881 sbcfung 5206 csbfv12g 5516 csbfv2g 5517 elfvmptrab 5575 csbov12g 5872 csbov1g 5873 csbov2g 5874 |
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