Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pm3.31 | GIF version |
Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.) |
Ref | Expression |
---|---|
pm3.31 | ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → 𝜒))) | |
2 | 1 | impd 252 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 |
This theorem is referenced by: impexp 261 imp5a 356 equsexd 1722 mo3h 2072 rexim 2564 peano5 4580 issref 4991 bj-indind 13927 |
Copyright terms: Public domain | W3C validator |