Theorem csbconstg 3139

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3138 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 2372	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3138	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1395   ∈ wcel 2200  ⦋csb 3125

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2802  df-sbc 3030  df-csb 3126

This theorem is referenced by:  sbcel1g  3144  sbceq1g  3145  sbcel2g  3146  sbceq2g  3147  csbidmg  3182  sbcbr12g  4142  sbcbr1g  4143  sbcbr2g  4144  sbcrel  4810  csbcnvg  4912  csbresg  5014  sbcfung  5348  csbfv12g  5675  csbfv2g  5676  elfvmptrab  5738  csbov12g  6053  csbov1g  6054  csbov2g  6055  csbwrdg  11136