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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2an | Structured version Visualization version GIF version |
Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd2an | ⊢ (( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ((𝜑 ∧ 𝜓) → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vd1 42190 | . 2 ⊢ (( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ (( 𝜑 , 𝜓 ) → 𝜒)) | |
2 | df-vhc2 42201 | . . 3 ⊢ (( 𝜑 , 𝜓 ) ↔ (𝜑 ∧ 𝜓)) | |
3 | 2 | imbi1i 350 | . 2 ⊢ ((( 𝜑 , 𝜓 ) → 𝜒) ↔ ((𝜑 ∧ 𝜓) → 𝜒)) |
4 | 1, 3 | bitri 274 | 1 ⊢ (( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ((𝜑 ∧ 𝜓) → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ wa 396 ( wvd1 42189 ( wvhc2 42200 |
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 df-vhc2 42201 |
This theorem is referenced by: dfvd2ani 42203 dfvd2anir 42204 iden2 42234 |
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