Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > expdimp | GIF version |
Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008.) |
Ref | Expression |
---|---|
exp3a.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Ref | Expression |
---|---|
expdimp | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp3a.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) | |
2 | 1 | expd 245 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | imp 115 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
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 is referenced by: rexlimdvv 2439 reu6 2730 fun11iun 5147 poxp 5853 smoel 5915 iinerm 6178 prarloclemlo 6592 peano5uzti 8346 lbzbi 8551 ssfzo12bi 9081 cau3lem 9710 nn0seqcvgd 9880 |
Copyright terms: Public domain | W3C validator |