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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd3ir | Structured version Visualization version GIF version |
Description: Right-to-left inference form of dfvd3 41825. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd3ir.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
dfvd3ir | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd3ir.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | dfvd3 41825 | . 2 ⊢ (( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃)))) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd3 41821 |
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 1091 df-vd3 41824 |
This theorem is referenced by: vd03 41833 vd13 41835 vd23 41836 in3an 41845 idn3 41849 gen31 41855 e223 41869 e333 41967 e233 41999 e323 42000 |
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