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Mirrors > Home > MPE Home > Th. List > Mathboxes > vd13 | Structured version Visualization version GIF version |
Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and a two additional hypotheses. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vd13.1 | ⊢ ( 𝜑 ▶ 𝜓 ) |
Ref | Expression |
---|---|
vd13 | ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vd13.1 | . . . . 5 ⊢ ( 𝜑 ▶ 𝜓 ) | |
2 | 1 | in1 41277 | . . . 4 ⊢ (𝜑 → 𝜓) |
3 | 2 | a1d 25 | . . 3 ⊢ (𝜑 → (𝜒 → 𝜓)) |
4 | 3 | a1dd 50 | . 2 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜓))) |
5 | 4 | dfvd3ir 41299 | 1 ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜓 ) |
Colors of variables: wff setvar class |
Syntax hints: ( wvd1 41275 ( wvd3 41293 |
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 210 df-an 400 df-3an 1086 df-vd1 41276 df-vd3 41296 |
This theorem is referenced by: e13 41454 e31 41457 e123 41468 |
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