Metamath Proof Explorer
Description: Inference associated with bj-imim21 . Its associated inference is
syl5 . (Contributed by BJ, 19-Jul-2019)
|
|
Ref |
Expression |
|
Hypothesis |
bj-imim21i.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
bj-imim21i |
⊢ ( ( 𝜒 → ( 𝜓 → 𝜃 ) ) → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
bj-imim21i.1 |
⊢ ( 𝜑 → 𝜓 ) |
2 |
|
bj-imim21 |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → ( 𝜓 → 𝜃 ) ) → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) ) |
3 |
1 2
|
ax-mp |
⊢ ( ( 𝜒 → ( 𝜓 → 𝜃 ) ) → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) |