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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2ir | Structured version Visualization version GIF version |
Description: Right-to-left inference form of dfvd2 40911. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd2ir.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
dfvd2ir | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd2ir.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | dfvd2 40911 | . 2 ⊢ (( 𝜑 , 𝜓 ▶ 𝜒 ) ↔ (𝜑 → (𝜓 → 𝜒))) | |
3 | 1, 2 | mpbir 233 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 40909 |
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 40910 |
This theorem is referenced by: vd02 40930 vd12 40932 in2an 40940 in3 40941 idn2 40945 gen21 40951 gen21nv 40952 gen22 40954 e2 40963 e222 40968 |
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