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Mirrors > Home > MPE Home > Th. List > orass | Structured version Visualization version GIF version |
Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
orass | ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 869 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑 ∨ 𝜓))) | |
2 | or12 920 | . 2 ⊢ ((𝜒 ∨ (𝜑 ∨ 𝜓)) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓))) | |
3 | orcom 869 | . . 3 ⊢ ((𝜒 ∨ 𝜓) ↔ (𝜓 ∨ 𝜒)) | |
4 | 3 | orbi2i 912 | . 2 ⊢ ((𝜑 ∨ (𝜒 ∨ 𝜓)) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
5 | 1, 2, 4 | 3bitri 297 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∨ wo 846 |
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 847 |
This theorem is referenced by: pm2.31 922 pm2.32 923 or32 925 or4 926 3orass 1091 axi12 2706 axbnd 2707 unass 4131 tppreqb 4770 ltxr 13043 lcmass 16497 plydivex 25673 clwwlkneq0 29015 disjxpin 31548 wl-ifpimpr 35966 impor 36569 ifpim123g 41846 |
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