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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2ani | Structured version Visualization version GIF version |
Description: Inference form of dfvd2an 42172. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd2ani.1 | ⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) |
Ref | Expression |
---|---|
dfvd2ani | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd2ani.1 | . 2 ⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) | |
2 | dfvd2an 42172 | . 2 ⊢ (( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ((𝜑 ∧ 𝜓) → 𝜒)) | |
3 | 1, 2 | mpbi 229 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ( wvd1 42159 ( wvhc2 42170 |
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 42160 df-vhc2 42171 |
This theorem is referenced by: int2 42196 el021old 42291 el2122old 42309 un0.1 42369 un10 42378 un01 42379 |
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