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Mirrors > Home > ILE Home > Th. List > csbeq2i | GIF version |
Description: Formula-building inference rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
csbeq2i.1 | ⊢ 𝐵 = 𝐶 |
Ref | Expression |
---|---|
csbeq2i | ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq2i.1 | . . . 4 ⊢ 𝐵 = 𝐶 | |
2 | 1 | a1i 9 | . . 3 ⊢ (⊤ → 𝐵 = 𝐶) |
3 | 2 | csbeq2dv 2875 | . 2 ⊢ (⊤ → ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶) |
4 | 3 | trud 1252 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1243 ⊤wtru 1244 ⦋csb 2852 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: csbvarg 2877 csbnest1g 2901 csbsng 3431 csbunig 3588 csbxpg 4421 csbcnvg 4519 csbdmg 4529 csbresg 4615 csbrng 4782 csbfv12g 5209 csbnegg 7209 |
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