Theorem csbconstg 3083

Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 3082 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 2329	. 2 ⊢ Ⅎ𝑥𝐵
2	1	csbconstgf 3082	1 ⊢ (𝐴 ∈ 𝑉 → ⦋𝐴 / 𝑥⦌𝐵 = 𝐵)

Syntax hints:   → wi 4   = wceq 1363   ∈ wcel 2158  ⦋csb 3069

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-sbc 2975  df-csb 3070

This theorem is referenced by:  sbcel1g  3088  sbceq1g  3089  sbcel2g  3090  sbceq2g  3091  csbidmg  3125  sbcbr12g  4070  sbcbr1g  4071  sbcbr2g  4072  sbcrel  4724  csbcnvg  4823  csbresg  4922  sbcfung  5252  csbfv12g  5564  csbfv2g  5565  elfvmptrab  5624  csbov12g  5927  csbov1g  5928  csbov2g  5929