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Mirrors > Home > ILE Home > Th. List > csbeq2i | GIF version |
Description: Formula-building inference 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 3028 | . 2 ⊢ (⊤ → ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶) |
4 | 3 | mptru 1340 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ⊤wtru 1332 ⦋csb 3003 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: csbvarg 3030 csbnest1g 3055 csbsng 3584 csbunig 3744 csbxpg 4620 csbcnvg 4723 csbdmg 4733 csbresg 4822 csbrng 5000 csbfv12g 5457 csbnegg 7960 iseqf1olemjpcl 10268 iseqf1olemqpcl 10269 iseqf1olemfvp 10270 seq3f1olemqsum 10273 |
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