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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd3ani | Structured version Visualization version GIF version |
Description: Inference form of dfvd3an 41018. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd3ani.1 | ⊢ ( ( 𝜑 , 𝜓 , 𝜒 ) ▶ 𝜃 ) |
Ref | Expression |
---|---|
dfvd3ani | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd3ani.1 | . 2 ⊢ ( ( 𝜑 , 𝜓 , 𝜒 ) ▶ 𝜃 ) | |
2 | dfvd3an 41018 | . 2 ⊢ (( ( 𝜑 , 𝜓 , 𝜒 ) ▶ 𝜃 ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)) | |
3 | 1, 2 | mpbi 232 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1083 ( wvd1 40993 ( wvhc3 41012 |
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 209 df-vd1 40994 df-vhc3 41013 |
This theorem is referenced by: int3 41036 el0321old 41141 |
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