Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2i | Structured version Visualization version GIF version |
Description: Inference form of dfvd2 37816. (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 37816 | . 2 ⊢ (( 𝜑 , 𝜓 ▶ 𝜒 ) ↔ (𝜑 → (𝜓 → 𝜒))) | |
3 | 1, 2 | mpbi 219 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 37814 |
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 196 df-an 385 df-vd2 37815 |
This theorem is referenced by: vd23 37848 in2 37851 in2an 37854 gen21 37865 gen21nv 37866 gen22 37868 exinst 37870 exinst01 37871 exinst11 37872 e2 37877 e222 37882 e233 38013 e323 38014 |
Copyright terms: Public domain | W3C validator |