![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > sbid2 | GIF version |
Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
sbid2.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
sbid2 | ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbid2.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nfri 1530 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | 2 | sbid2h 1860 | 1 ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 105 Ⅎwnf 1471 [wsb 1773 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: sbco4lem 2018 |
Copyright terms: Public domain | W3C validator |