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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2imp | Structured version Visualization version GIF version |
Description: The virtual deduction form of a 2-antecedent nested implication implies the 2-antecedent nested implication. (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd2imp | ⊢ (( 𝜑 , 𝜓 ▶ 𝜒 ) → (𝜑 → (𝜓 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd2 41901 | . 2 ⊢ (( 𝜑 , 𝜓 ▶ 𝜒 ) ↔ (𝜑 → (𝜓 → 𝜒))) | |
2 | 1 | biimpi 219 | 1 ⊢ (( 𝜑 , 𝜓 ▶ 𝜒 ) → (𝜑 → (𝜓 → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 41899 |
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-vd2 41900 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |