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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 3070 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 2319 | . 2 ⊢ Ⅎ𝑥𝐵 | |
2 | 1 | csbconstgf 3070 | 1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1353 ∈ wcel 2148 ⦋csb 3057 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-sbc 2963 df-csb 3058 |
This theorem is referenced by: sbcel1g 3076 sbceq1g 3077 sbcel2g 3078 sbceq2g 3079 csbidmg 3113 sbcbr12g 4058 sbcbr1g 4059 sbcbr2g 4060 sbcrel 4712 csbcnvg 4811 csbresg 4910 sbcfung 5240 csbfv12g 5551 csbfv2g 5552 elfvmptrab 5611 csbov12g 5913 csbov1g 5914 csbov2g 5915 |
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