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Mirrors > Home > MPE Home > Th. List > Mathboxes > e001 | 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 |
---|---|
e001.1 | ⊢ 𝜑 |
e001.2 | ⊢ 𝜓 |
e001.3 | ⊢ ( 𝜒 ▶ 𝜃 ) |
e001.4 | ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏))) |
Ref | Expression |
---|---|
e001 | ⊢ ( 𝜒 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e001.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | vd01 42217 | . 2 ⊢ ( 𝜒 ▶ 𝜑 ) |
3 | e001.2 | . . 3 ⊢ 𝜓 | |
4 | 3 | vd01 42217 | . 2 ⊢ ( 𝜒 ▶ 𝜓 ) |
5 | e001.3 | . 2 ⊢ ( 𝜒 ▶ 𝜃 ) | |
6 | e001.4 | . 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏))) | |
7 | 2, 4, 5, 6 | e111 42294 | 1 ⊢ ( 𝜒 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd1 42189 |
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-vd1 42190 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |