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Mirrors > Home > MPE Home > Th. List > Mathboxes > e002 | 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 |
---|---|
e002.1 | ⊢ 𝜑 |
e002.2 | ⊢ 𝜓 |
e002.3 | ⊢ ( 𝜒 , 𝜃 ▶ 𝜏 ) |
e002.4 | ⊢ (𝜑 → (𝜓 → (𝜏 → 𝜂))) |
Ref | Expression |
---|---|
e002 | ⊢ ( 𝜒 , 𝜃 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e002.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | vd02 42188 | . 2 ⊢ ( 𝜒 , 𝜃 ▶ 𝜑 ) |
3 | e002.2 | . . 3 ⊢ 𝜓 | |
4 | 3 | vd02 42188 | . 2 ⊢ ( 𝜒 , 𝜃 ▶ 𝜓 ) |
5 | e002.3 | . 2 ⊢ ( 𝜒 , 𝜃 ▶ 𝜏 ) | |
6 | e002.4 | . 2 ⊢ (𝜑 → (𝜓 → (𝜏 → 𝜂))) | |
7 | 2, 4, 5, 6 | e222 42226 | 1 ⊢ ( 𝜒 , 𝜃 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 42167 |
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-vd2 42168 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |