Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pm5.74d | GIF version |
Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 21-Mar-1996.) |
Ref | Expression |
---|---|
pm5.74d.1 | ⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃))) |
Ref | Expression |
---|---|
pm5.74d | ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.74d.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃))) | |
2 | pm5.74 178 | . 2 ⊢ ((𝜓 → (𝜒 ↔ 𝜃)) ↔ ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) | |
3 | 1, 2 | sylib 121 | 1 ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: imbi2d 229 imim21b 251 pm5.74da 441 cbval2 1914 dfiin2g 3904 brecop 6599 dom2lem 6746 nn0ind-raph 9316 |
Copyright terms: Public domain | W3C validator |