Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > imdistanda | GIF version |
Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011.) |
Ref | Expression |
---|---|
imdistanda.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Ref | Expression |
---|---|
imdistanda | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imdistanda.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) | |
2 | 1 | ex 113 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | imdistand 435 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜃))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: fzind 8462 uzss 8639 qbtwnzlemshrink 9258 rebtwn2zlemshrink 9262 cau3lem 10000 |
Copyright terms: Public domain | W3C validator |