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Mirrors > Home > MPE Home > Th. List > pm1.5 | Structured version Visualization version GIF version |
Description: Axiom *1.5 (Assoc) of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm1.5 | ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 864 | . . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒)) | |
2 | 1 | olcd 871 | . 2 ⊢ (𝜑 → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
3 | olc 865 | . . 3 ⊢ (𝜒 → (𝜑 ∨ 𝜒)) | |
4 | 3 | orim2i 908 | . 2 ⊢ ((𝜓 ∨ 𝜒) → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
5 | 2, 4 | jaoi 854 | 1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 844 |
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 206 df-or 845 |
This theorem is referenced by: or12 918 meran1 34588 meran3 34590 |
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