Theorem csbconstg 3016

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3015 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 2281	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3015	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1331   ∈ wcel 1480  ⦋csb 3003

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 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910  df-csb 3004

This theorem is referenced by:  sbcel1g  3021  sbceq1g  3022  sbcel2g  3023  sbceq2g  3024  csbidmg  3056  sbcbr12g  3983  sbcbr1g  3984  sbcbr2g  3985  sbcrel  4625  csbcnvg  4723  csbresg  4822  sbcfung  5147  csbfv12g  5457  csbfv2g  5458  elfvmptrab  5516  csbov12g  5810  csbov1g  5811  csbov2g  5812