This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Commuted form of expd . (Contributed by Alan Sare, 18-Mar-2012)
Shorten expd . (Revised by Wolf Lammen, 28-Jul-2022)
|
|
Ref |
Expression |
|
Hypothesis |
expd.1 |
⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ) |
|
Assertion |
expdcom |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
expd.1 |
⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ) |
| 2 |
1
|
com12 |
⊢ ( ( 𝜓 ∧ 𝜒 ) → ( 𝜑 → 𝜃 ) ) |
| 3 |
2
|
ex |
⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) |