![]() |
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 143 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
3 | 2 | spimv 1784 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 ∀wal 1330 |
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 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: spvv 1880 chvarv 1910 ru 2912 nalset 4066 tfisi 4509 tfr1onlemsucfn 6245 tfr1onlemsucaccv 6246 tfr1onlembxssdm 6248 tfr1onlembfn 6249 tfr1onlemres 6254 tfri1dALT 6256 tfrcllemsucfn 6258 tfrcllemsucaccv 6259 tfrcllembxssdm 6261 tfrcllembfn 6262 tfrcllemres 6267 findcard2 6791 findcard2s 6792 bj-nalset 13264 |
Copyright terms: Public domain | W3C validator |