Theorem csbconstg 3094

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3093 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 2336	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3093	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1364   ∈ wcel 2164  ⦋csb 3080

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 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-sbc 2986  df-csb 3081

This theorem is referenced by:  sbcel1g  3099  sbceq1g  3100  sbcel2g  3101  sbceq2g  3102  csbidmg  3137  sbcbr12g  4084  sbcbr1g  4085  sbcbr2g  4086  sbcrel  4745  csbcnvg  4846  csbresg  4945  sbcfung  5278  csbfv12g  5592  csbfv2g  5593  elfvmptrab  5653  csbov12g  5957  csbov1g  5958  csbov2g  5959  csbwrdg  10943