Theorem csbconstg 3108

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3107 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 2349	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3107	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1373   ∈ wcel 2177  ⦋csb 3094

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-sbc 3000  df-csb 3095

This theorem is referenced by:  sbcel1g  3113  sbceq1g  3114  sbcel2g  3115  sbceq2g  3116  csbidmg  3151  sbcbr12g  4103  sbcbr1g  4104  sbcbr2g  4105  sbcrel  4765  csbcnvg  4866  csbresg  4967  sbcfung  5300  csbfv12g  5621  csbfv2g  5622  elfvmptrab  5682  csbov12g  5991  csbov1g  5992  csbov2g  5993  csbwrdg  11030