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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd3an | Structured version Visualization version GIF version |
Description: Definition of a 3-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd3an | ⊢ (( ( 𝜑 , 𝜓 , 𝜒 ) ▶ 𝜃 ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vd1 41863 | . 2 ⊢ (( ( 𝜑 , 𝜓 , 𝜒 ) ▶ 𝜃 ) ↔ (( 𝜑 , 𝜓 , 𝜒 ) → 𝜃)) | |
2 | df-vhc3 41882 | . . 3 ⊢ (( 𝜑 , 𝜓 , 𝜒 ) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒)) | |
3 | 2 | imbi1i 353 | . 2 ⊢ ((( 𝜑 , 𝜓 , 𝜒 ) → 𝜃) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)) |
4 | 1, 3 | bitri 278 | 1 ⊢ (( ( 𝜑 , 𝜓 , 𝜒 ) ▶ 𝜃 ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∧ w3a 1089 ( wvd1 41862 ( wvhc3 41881 |
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-vd1 41863 df-vhc3 41882 |
This theorem is referenced by: dfvd3ani 41888 dfvd3anir 41889 |
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