Theorem csbeq2i 3108

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 9	. . 3 ⊢ (⊤ → 𝐵 = 𝐶)
3	2	csbeq2dv 3107	. 2 ⊢ (⊤ → ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶)
4	3	mptru 1373	1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶

Syntax hints:   = wceq 1364  ⊤wtru 1365  ⦋csb 3081

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-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-sbc 2987  df-csb 3082

This theorem is referenced by:  csbvarg  3109  csbnest1g  3137  csbsng  3680  csbunig  3844  csbxpg  4741  csbcnvg  4847  csbdmg  4857  csbresg  4946  csbrng  5128  csbfv12g  5593  csbnegg  8219  iseqf1olemjpcl  10582  iseqf1olemqpcl  10583  iseqf1olemfvp  10584  seq3f1olemqsum  10587  csbwrdg  10946