Theorem csbconstg 3063

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3062 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 2312	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3062	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1348   ∈ wcel 2141  ⦋csb 3049

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-sbc 2956  df-csb 3050

This theorem is referenced by:  sbcel1g  3068  sbceq1g  3069  sbcel2g  3070  sbceq2g  3071  csbidmg  3105  sbcbr12g  4044  sbcbr1g  4045  sbcbr2g  4046  sbcrel  4697  csbcnvg  4795  csbresg  4894  sbcfung  5222  csbfv12g  5532  csbfv2g  5533  elfvmptrab  5591  csbov12g  5892  csbov1g  5893  csbov2g  5894