![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 2994 | . 2 ⊢ (⊤ → ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶) |
4 | 3 | mptru 1323 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1314 ⊤wtru 1315 ⦋csb 2971 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-11 1467 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-sbc 2879 df-csb 2972 |
This theorem is referenced by: csbvarg 2996 csbnest1g 3021 csbsng 3550 csbunig 3710 csbxpg 4580 csbcnvg 4683 csbdmg 4693 csbresg 4780 csbrng 4958 csbfv12g 5411 csbnegg 7883 iseqf1olemjpcl 10161 iseqf1olemqpcl 10162 iseqf1olemfvp 10163 seq3f1olemqsum 10166 |
Copyright terms: Public domain | W3C validator |