Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pm5.74da | GIF version |
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 4-May-2007.) |
Ref | Expression |
---|---|
pm5.74da.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ↔ 𝜃)) |
Ref | Expression |
---|---|
pm5.74da | ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.74da.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ↔ 𝜃)) | |
2 | 1 | ex 108 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃))) |
3 | 2 | pm5.74d 171 | 1 ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: ralbida 2320 elrab3t 2697 dff13 5407 |
Copyright terms: Public domain | W3C validator |