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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 908 | 1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 847 |
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 848 |
This theorem is referenced by: 19.34 1984 r19.45v 3191 nnm1nn0 12565 elfzo0l 13792 xrge0iifhom 33898 fmla1 35372 bj-andnotim 36571 orfa2 38073 expdioph 43012 ifpimim 43499 simpcntrab 46826 |
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