Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfsbc1 | GIF version |
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfsbc1.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfsbc1 | ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfsbc1.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | 2 | nfsbc1d 2831 | . 2 ⊢ (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑) |
4 | 3 | trud 1293 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1285 Ⅎwnf 1389 Ⅎwnfc 2206 [wsbc 2815 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-sbc 2816 |
This theorem is referenced by: nfsbc1v 2833 riotass2 5514 riotass 5515 bj-intabssel 10599 |
Copyright terms: Public domain | W3C validator |