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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 2971 | . 2 ⊢ (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑) |
4 | 3 | mptru 1357 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1349 Ⅎwnf 1453 Ⅎwnfc 2299 [wsbc 2955 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-sbc 2956 |
This theorem is referenced by: nfsbc1v 2973 riotass2 5835 riotass 5836 bj-intabssel 13824 |
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