Theorem csbconstg 2858

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.)

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 2175	. 2 ⊢ ℲxB
2	1	csbconstgf 2857	1 ⊢ (A ∈ 𝑉 → ⦋A / x⦌B = B)

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