Theorem csbeq2i 3084

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 3083	. 2 ⊢ (⊤ → ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶)
4	3	mptru 1362	1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶

Syntax hints:   = wceq 1353  ⊤wtru 1354  ⦋csb 3057

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-sbc 2963  df-csb 3058

This theorem is referenced by:  csbvarg  3085  csbnest1g  3112  csbsng  3653  csbunig  3817  csbxpg  4707  csbcnvg  4811  csbdmg  4821  csbresg  4910  csbrng  5090  csbfv12g  5551  csbnegg  8154  iseqf1olemjpcl  10494  iseqf1olemqpcl  10495  iseqf1olemfvp  10496  seq3f1olemqsum  10499