Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > spv | GIF version |
Description: Specialization, using implicit substitition. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
spv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
spv | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spv.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
2 | 1 | biimpd 142 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
3 | 2 | spimv 1732 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 103 ∀wal 1282 |
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-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: chvarv 1853 ru 2814 nalset 3908 tfisi 4328 findcard2 6373 findcard2s 6374 bj-nalset 10686 |
Copyright terms: Public domain | W3C validator |