![]() |
Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > e02an | Structured version Visualization version GIF version |
Description: Conjunction form of e02 37943. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e02an.1 | ⊢ 𝜑 |
e02an.2 | ⊢ ( 𝜓 , 𝜒 ▶ 𝜃 ) |
e02an.3 | ⊢ ((𝜑 ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
e02an | ⊢ ( 𝜓 , 𝜒 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e02an.1 | . 2 ⊢ 𝜑 | |
2 | e02an.2 | . 2 ⊢ ( 𝜓 , 𝜒 ▶ 𝜃 ) | |
3 | e02an.3 | . . 3 ⊢ ((𝜑 ∧ 𝜃) → 𝜏) | |
4 | 3 | ex 449 | . 2 ⊢ (𝜑 → (𝜃 → 𝜏)) |
5 | 1, 2, 4 | e02 37943 | 1 ⊢ ( 𝜓 , 𝜒 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ( wvd2 37814 |
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 196 df-an 385 df-vd2 37815 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |