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| Mirrors > Home > MPE Home > Th. List > orim1i | Structured version Visualization version GIF version | ||
| Description: Introduce disjunct to both sides of an implication. (Contributed by NM, 6-Jun-1994.) | 
| Ref | Expression | 
|---|---|
| orim1i.1 | ⊢ (𝜑 → 𝜓) | 
| Ref | Expression | 
|---|---|
| orim1i | ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | orim1i.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | id 22 | . 2 ⊢ (𝜒 → 𝜒) | |
| 3 | 1, 2 | orim12i 909 | 1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒)) | 
| 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: 19.34 1986 r19.45v 3193 nnm1nn0 12567 elfzo0l 13795 xrge0iifhom 33936 fmla1 35392 bj-andnotim 36589 orfa2 38093 expdioph 43035 ifpimim 43522 simpcntrab 46885 | 
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