Theorem csbeq2i 3859

Description: Formula-building inference for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)

Hypothesis

Ref	Expression
csbeq2i.1	⊢ 𝐵 = 𝐶

Assertion

Ref	Expression
csbeq2i	⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶

Proof of Theorem csbeq2i

Step	Hyp	Ref	Expression
1		csbeq2i.1	. . . 4 ⊢ 𝐵 = 𝐶
2	1	a1i 11	. . 3 ⊢ (⊤ → 𝐵 = 𝐶)
3	2	csbeq2dv 3858	. 2 ⊢ (⊤ → ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶)
4	3	mptru 1549	1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶

Syntax hints:   = wceq 1542  ⊤wtru 1543  ⦋csb 3851

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-sbc 3743  df-csb 3852

This theorem is referenced by:  csbnest1g  4386  csbvarg  4388  csbsng  4667  csbprg  4668  csbopg  4849  csbuni  4895  csbmpt12  5513  csbxp  5733  csbcnv  5840  csbcnvgALT  5841  csbdm  5854  csbres  5949  csbrn  6169  csbpredg  6273  csbfv12  6887  fvmpocurryd  8223  csbfrecsg  8236  csbwrecsg  8270  csbnegg  11389  csbwrdg  14479  matgsum  22393  precsexlemcbv  28214  precsexlem3  28217  disjxpin  32674  f1od2  32808  sumeq2si  36415  prodeq2si  36417  bj-csbsn  37146  csbrecsg  37577  csbrdgg  37578  csboprabg  37579  csbmpo123  37580  csbfinxpg  37637  poimirlem24  37889  cdleme31so  40749  cdleme31sn  40750  cdleme31sn1  40751  cdleme31se  40752  cdleme31se2  40753  cdleme31sc  40754  cdleme31sde  40755  cdleme31sn2  40759  cdlemkid3N  41303  cdlemkid4  41304  climinf2mpt  46066  climinfmpt  46067