Theorem csbconstg 3090

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3089 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 2332	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3089	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1364   ∈ wcel 2160  ⦋csb 3076

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2758  df-sbc 2982  df-csb 3077

This theorem is referenced by:  sbcel1g  3095  sbceq1g  3096  sbcel2g  3097  sbceq2g  3098  csbidmg  3132  sbcbr12g  4080  sbcbr1g  4081  sbcbr2g  4082  sbcrel  4737  csbcnvg  4836  csbresg  4935  sbcfung  5266  csbfv12g  5579  csbfv2g  5580  elfvmptrab  5639  csbov12g  5943  csbov1g  5944  csbov2g  5945