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Mirrors > Home > MPE Home > Th. List > pm3.3 | Structured version Visualization version GIF version |
Description: Theorem *3.3 (Exp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.) |
Ref | Expression |
---|---|
pm3.3 | ⊢ (((𝜑 ∧ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) → ((𝜑 ∧ 𝜓) → 𝜒)) | |
2 | 1 | expd 451 | 1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: impexp 461 pm4.79 605 trer 31480 bj-alanim 31781 bj-mo3OLD 32022 wl-mo3t 32537 trsbc 37771 simplbi2VD 38103 exbirVD 38110 exbiriVD 38111 3impexpVD 38113 trsbcVD 38135 simplbi2comtVD 38146 |
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