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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 867 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑 ∨ 𝜓))) | |
2 | or12 918 | . 2 ⊢ ((𝜒 ∨ (𝜑 ∨ 𝜓)) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓))) | |
3 | orcom 867 | . . 3 ⊢ ((𝜒 ∨ 𝜓) ↔ (𝜓 ∨ 𝜒)) | |
4 | 3 | orbi2i 910 | . 2 ⊢ ((𝜑 ∨ (𝜒 ∨ 𝜓)) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
5 | 1, 2, 4 | 3bitri 300 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∨ 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 210 df-or 845 |
This theorem is referenced by: pm2.31 920 pm2.32 921 or32 923 or4 924 3orass 1087 axi12 2768 axbnd 2769 unass 4093 tppreqb 4698 ltxr 12498 lcmass 15948 plydivex 24893 clwwlkneq0 27814 disjxpin 30351 wl-ifpimpr 34883 impor 35519 ifpim123g 40208 |
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