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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2i | Structured version Visualization version GIF version |
Description: Inference form of dfvd2 40906. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd2i.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
Ref | Expression |
---|---|
dfvd2i | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd2i.1 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | dfvd2 40906 | . 2 ⊢ (( 𝜑 , 𝜓 ▶ 𝜒 ) ↔ (𝜑 → (𝜓 → 𝜒))) | |
3 | 1, 2 | mpbi 232 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 40904 |
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-an 399 df-vd2 40905 |
This theorem is referenced by: vd23 40929 in2 40932 in2an 40935 gen21 40946 gen21nv 40947 gen22 40949 exinst 40951 exinst01 40952 exinst11 40953 e2 40958 e222 40963 e233 41092 e323 41093 |
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