Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > el0321old | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
el0321old.1 | ⊢ 𝜑 |
el0321old.2 | ⊢ ( ( 𝜓 , 𝜒 , 𝜃 ) ▶ 𝜏 ) |
el0321old.3 | ⊢ ((𝜑 ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
el0321old | ⊢ ( ( 𝜓 , 𝜒 , 𝜃 ) ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | el0321old.1 | . . 3 ⊢ 𝜑 | |
2 | el0321old.2 | . . . 4 ⊢ ( ( 𝜓 , 𝜒 , 𝜃 ) ▶ 𝜏 ) | |
3 | 2 | dfvd3ani 37832 | . . 3 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
4 | el0321old.3 | . . 3 ⊢ ((𝜑 ∧ 𝜏) → 𝜂) | |
5 | 1, 3, 4 | eel0321old 37962 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜂) |
6 | 5 | dfvd3anir 37833 | 1 ⊢ ( ( 𝜓 , 𝜒 , 𝜃 ) ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ( wvd1 37806 ( wvhc3 37825 |
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-vd1 37807 df-vhc3 37826 |
This theorem is referenced by: suctrALTcfVD 38181 |
Copyright terms: Public domain | W3C validator |