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Mirrors > Home > ILE Home > Th. List > orim1i | 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 19 | . 2 ⊢ (𝜒 → 𝜒) | |
3 | 1, 2 | orim12i 754 | 1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 703 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: 19.34 1677 dveeq2or 1809 sbequilem 1831 sbequi 1832 dvelimALT 2003 dvelimfv 2004 dvelimor 2011 r19.45av 2630 acexmidlemcase 5845 omniwomnimkv 7139 nnm1nn0 9163 prmdc 12071 triap 13983 |
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