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Mirrors > Home > MPE Home > Th. List > Mathboxes > e122 | 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 |
---|---|
e122.1 | ⊢ ( 𝜑 ▶ 𝜓 ) |
e122.2 | ⊢ ( 𝜑 , 𝜒 ▶ 𝜃 ) |
e122.3 | ⊢ ( 𝜑 , 𝜒 ▶ 𝜏 ) |
e122.4 | ⊢ (𝜓 → (𝜃 → (𝜏 → 𝜂))) |
Ref | Expression |
---|---|
e122 | ⊢ ( 𝜑 , 𝜒 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e122.1 | . . 3 ⊢ ( 𝜑 ▶ 𝜓 ) | |
2 | 1 | vd12 42201 | . 2 ⊢ ( 𝜑 , 𝜒 ▶ 𝜓 ) |
3 | e122.2 | . 2 ⊢ ( 𝜑 , 𝜒 ▶ 𝜃 ) | |
4 | e122.3 | . 2 ⊢ ( 𝜑 , 𝜒 ▶ 𝜏 ) | |
5 | e122.4 | . 2 ⊢ (𝜓 → (𝜃 → (𝜏 → 𝜂))) | |
6 | 2, 3, 4, 5 | e222 42237 | 1 ⊢ ( 𝜑 , 𝜒 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd1 42170 ( wvd2 42178 |
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 397 df-vd1 42171 df-vd2 42179 |
This theorem is referenced by: tratrbVD 42462 |
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