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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 760 | 1 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ∨ 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 709 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: 19.34 1695 dveeq2or 1827 sbequilem 1849 sbequi 1850 dvelimALT 2022 dvelimfv 2023 dvelimor 2030 r19.45av 2650 acexmidlemcase 5891 omniwomnimkv 7195 nnm1nn0 9247 prmdc 12162 pcadd2 12373 triap 15236 |
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