Theorem csbconstg 3118

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3117 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 2352	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3117	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1375   ∈ wcel 2180  ⦋csb 3104

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 713  ax-5 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-10 1531  ax-11 1532  ax-i12 1533  ax-bndl 1535  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-i5r 1561  ax-ext 2191

This theorem depends on definitions:  df-bi 117  df-tru 1378  df-nf 1487  df-sb 1789  df-clab 2196  df-cleq 2202  df-clel 2205  df-nfc 2341  df-v 2781  df-sbc 3009  df-csb 3105

This theorem is referenced by:  sbcel1g  3123  sbceq1g  3124  sbcel2g  3125  sbceq2g  3126  csbidmg  3161  sbcbr12g  4118  sbcbr1g  4119  sbcbr2g  4120  sbcrel  4782  csbcnvg  4883  csbresg  4984  sbcfung  5318  csbfv12g  5641  csbfv2g  5642  elfvmptrab  5703  csbov12g  6014  csbov1g  6015  csbov2g  6016  csbwrdg  11067