Theorem csbconstg 3098

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3097 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 2339	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3097	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1364   ∈ wcel 2167  ⦋csb 3084

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-sbc 2990  df-csb 3085

This theorem is referenced by:  sbcel1g  3103  sbceq1g  3104  sbcel2g  3105  sbceq2g  3106  csbidmg  3141  sbcbr12g  4088  sbcbr1g  4089  sbcbr2g  4090  sbcrel  4749  csbcnvg  4850  csbresg  4949  sbcfung  5282  csbfv12g  5596  csbfv2g  5597  elfvmptrab  5657  csbov12g  5961  csbov1g  5962  csbov2g  5963  csbwrdg  10964