Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pm3.43 | GIF version |
Description: Theorem *3.43 (Comp) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 27-Nov-2013.) |
Ref | Expression |
---|---|
pm3.43 | ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.43i 267 | . 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒)))) | |
2 | 1 | imp 122 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒))) |
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 is referenced by: jcab 567 sbequilem 1759 eqvinc 2718 eqvincg 2719 |
Copyright terms: Public domain | W3C validator |