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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 44304. (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 44304 | . 2 ⊢ (( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) ↔ (𝜑 → (𝜓 → (𝜒 → 𝜃)))) | |
3 | 1, 2 | mpbir 230 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd3 44300 |
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-an 395 df-3an 1086 df-vd3 44303 |
This theorem is referenced by: vd03 44312 vd13 44314 vd23 44315 in3an 44324 idn3 44328 gen31 44334 e223 44348 e333 44446 e233 44478 e323 44479 |
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