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Mirrors > Home > MPE Home > Th. List > jao1i | Structured version Visualization version GIF version |
Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010.) |
Ref | Expression |
---|---|
jao1i.1 | ⊢ (𝜓 → (𝜒 → 𝜑)) |
Ref | Expression |
---|---|
jao1i | ⊢ ((𝜑 ∨ 𝜓) → (𝜒 → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ (𝜑 → (𝜒 → 𝜑)) | |
2 | jao1i.1 | . 2 ⊢ (𝜓 → (𝜒 → 𝜑)) | |
3 | 1, 2 | jaoi 853 | 1 ⊢ ((𝜑 ∨ 𝜓) → (𝜒 → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 843 |
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 209 df-or 844 |
This theorem is referenced by: pm2.64 938 pm2.82 972 sorpssint 7453 preleqg 9072 ltlen 10735 elnnnn0b 11935 znnn0nn 12088 scshwfzeqfzo 14182 nn0enne 15722 dvdsprmpweqnn 16215 dvdsprmpweqle 16216 prmirred 20636 pmatcollpw3fi1 21390 2lgsoddprmlem3 25984 prtlem14 36004 |
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