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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 868 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑 ∨ 𝜓))) | |
2 | or12 919 | . 2 ⊢ ((𝜒 ∨ (𝜑 ∨ 𝜓)) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓))) | |
3 | orcom 868 | . . 3 ⊢ ((𝜒 ∨ 𝜓) ↔ (𝜓 ∨ 𝜒)) | |
4 | 3 | orbi2i 911 | . 2 ⊢ ((𝜑 ∨ (𝜒 ∨ 𝜓)) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
5 | 1, 2, 4 | 3bitri 296 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∨ wo 845 |
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 846 |
This theorem is referenced by: pm2.31 921 pm2.32 922 or32 924 or4 925 3orass 1090 axi12 2705 axbnd 2706 unass 4124 tppreqb 4763 ltxr 13028 lcmass 16482 plydivex 25641 clwwlkneq0 28859 disjxpin 31392 wl-ifpimpr 35904 impor 36507 ifpim123g 41714 |
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