Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cbval2v | GIF version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 4-Feb-2005.) |
Ref | Expression |
---|---|
cbval2v.1 | ⊢ ((𝑥 = 𝑧 ∧ 𝑦 = 𝑤) → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
cbval2v | ⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑧∀𝑤𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . 2 ⊢ Ⅎ𝑧𝜑 | |
2 | nfv 1508 | . 2 ⊢ Ⅎ𝑤𝜑 | |
3 | nfv 1508 | . 2 ⊢ Ⅎ𝑥𝜓 | |
4 | nfv 1508 | . 2 ⊢ Ⅎ𝑦𝜓 | |
5 | cbval2v.1 | . 2 ⊢ ((𝑥 = 𝑧 ∧ 𝑦 = 𝑤) → (𝜑 ↔ 𝜓)) | |
6 | 1, 2, 3, 4, 5 | cbval2 1891 | 1 ⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑧∀𝑤𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ↔ wb 104 ∀wal 1329 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |