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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 2869 | . 2 ⊢ ( ⊤ → ⦋A / x⦌B = ⦋A / x⦌𝐶) |
4 | 3 | trud 1251 | 1 ⊢ ⦋A / x⦌B = ⦋A / x⦌𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1242 ⊤ wtru 1243 ⦋csb 2846 |
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 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-sbc 2759 df-csb 2847 |
This theorem is referenced by: csbvarg 2871 csbnest1g 2895 csbsng 3422 csbunig 3579 csbxpg 4364 csbcnvg 4462 csbdmg 4472 csbresg 4558 csbrng 4725 csbfv12g 5152 csbnegg 7006 |
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