Theorem csbconstg 3059

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3058 with distinct variable requirement. (Contributed by Alan Sare, 22-Jul-2012.)

Assertion

Ref	Expression
csbconstg	⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Distinct variable group:   𝑥,𝐵

Allowed substitution hints:   𝐴(𝑥)   𝑉(𝑥)

Proof of Theorem csbconstg

Step	Hyp	Ref	Expression
1		nfcv 2308	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3058	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1343   ∈ wcel 2136  ⦋csb 3045

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-sbc 2952  df-csb 3046

This theorem is referenced by:  sbcel1g  3064  sbceq1g  3065  sbcel2g  3066  sbceq2g  3067  csbidmg  3101  sbcbr12g  4037  sbcbr1g  4038  sbcbr2g  4039  sbcrel  4690  csbcnvg  4788  csbresg  4887  sbcfung  5212  csbfv12g  5522  csbfv2g  5523  elfvmptrab  5581  csbov12g  5881  csbov1g  5882  csbov2g  5883