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 2953 | . 2 ⊢ (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑) |
4 | 3 | mptru 1344 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1336 Ⅎwnf 1440 Ⅎwnfc 2286 [wsbc 2937 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-sbc 2938 |
This theorem is referenced by: nfsbc1v 2955 riotass2 5807 riotass 5808 bj-intabssel 13405 |
Copyright terms: Public domain | W3C validator |