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Metamath Proof Explorer
Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010)
|
|
Ref |
Expression |
|
Hypothesis |
jao1i.1 |
⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) ) |
|
Assertion |
jao1i |
⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜒 → 𝜑 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
jao1i.1 |
⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) ) |
| 2 |
|
ax-1 |
⊢ ( 𝜑 → ( 𝜒 → 𝜑 ) ) |
| 3 |
2 1
|
jaoi |
⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜒 → 𝜑 ) ) |