Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pm5.35 | GIF version |
Description: Theorem *5.35 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm5.35 | ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ↔ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.1 591 | . 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → ((𝜑 → 𝜓) ↔ (𝜑 → 𝜒))) | |
2 | 1 | pm5.74rd 182 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ↔ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ↔ wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |