Theorem csbconstg 3011

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3010 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 2279	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3010	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1331   ∈ wcel 1480  ⦋csb 2998

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-sbc 2905  df-csb 2999

This theorem is referenced by:  sbcel1g  3016  sbceq1g  3017  sbcel2g  3018  sbceq2g  3019  csbidmg  3051  sbcbr12g  3978  sbcbr1g  3979  sbcbr2g  3980  sbcrel  4620  csbcnvg  4718  csbresg  4817  sbcfung  5142  csbfv12g  5450  csbfv2g  5451  elfvmptrab  5509  csbov12g  5803  csbov1g  5804  csbov2g  5805