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| Description: Axiom *1.4 of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.) | 
| Ref | Expression | 
|---|---|
| pm1.4 | ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | olc 869 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑)) | |
| 2 | orc 868 | . 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑)) | |
| 3 | 1, 2 | jaoi 858 | 1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∨ wo 848 | 
| 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 207 df-or 849 | 
| This theorem is referenced by: orcom 871 orcoms 873 pm2.3 925 pm2.36 972 pm2.37 973 rb-ax2 1753 prneimg 4854 cnf2dd 38098 orcomdd 38174 rp-fakeanorass 43526 orbi1rVD 44868 itsclc0yqsol 48685 | 
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