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Metamath Proof Explorer
Theorem a2i
Description: Inference distributing an antecedent. Inference associated with
ax-2 . Its associated inference is mpd . (Contributed by NM, 29-Dec-1992)
|
|
Ref |
Expression |
|
Hypothesis |
a2i.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
a2i |
⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
a2i.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
|
ax-2 |
⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) ) |
| 3 |
1 2
|
ax-mp |
⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) |