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Mirrors > Home > MPE Home > Th. List > pm5.3 | Structured version Visualization version GIF version |
Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.) |
Ref | Expression |
---|---|
pm5.3 | ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | impexp 462 | . 2 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ (𝜑 → (𝜓 → 𝜒))) | |
2 | imdistan 725 | . 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) ↔ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜒))) | |
3 | 1, 2 | bitri 264 | 1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ∧ wa 384 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 |
This theorem is referenced by: clss2lem 37918 |
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