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Mirrors > Home > MPE Home > Th. List > Mathboxes > e022 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e022.1 | ⊢ 𝜑 |
e022.2 | ⊢ ( 𝜓 , 𝜒 ▶ 𝜃 ) |
e022.3 | ⊢ ( 𝜓 , 𝜒 ▶ 𝜏 ) |
e022.4 | ⊢ (𝜑 → (𝜃 → (𝜏 → 𝜂))) |
Ref | Expression |
---|---|
e022 | ⊢ ( 𝜓 , 𝜒 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e022.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | vd02 42171 | . 2 ⊢ ( 𝜓 , 𝜒 ▶ 𝜑 ) |
3 | e022.2 | . 2 ⊢ ( 𝜓 , 𝜒 ▶ 𝜃 ) | |
4 | e022.3 | . 2 ⊢ ( 𝜓 , 𝜒 ▶ 𝜏 ) | |
5 | e022.4 | . 2 ⊢ (𝜑 → (𝜃 → (𝜏 → 𝜂))) | |
6 | 2, 3, 4, 5 | e222 42209 | 1 ⊢ ( 𝜓 , 𝜒 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 42150 |
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 206 df-an 396 df-vd2 42151 |
This theorem is referenced by: onfrALTVD 42464 |
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