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Mirrors > Home > MPE Home > Th. List > Mathboxes > e30 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e30.1 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
e30.2 | ⊢ 𝜏 |
e30.3 | ⊢ (𝜃 → (𝜏 → 𝜂)) |
Ref | Expression |
---|---|
e30 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e30.1 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) | |
2 | e30.2 | . . 3 ⊢ 𝜏 | |
3 | 2 | vd03 37845 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
4 | e30.3 | . 2 ⊢ (𝜃 → (𝜏 → 𝜂)) | |
5 | 1, 3, 4 | e33 37982 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd3 37824 |
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-3an 1033 df-vd3 37827 |
This theorem is referenced by: e30an 37994 |
Copyright terms: Public domain | W3C validator |