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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfvd2anir | Structured version Visualization version GIF version |
Description: Right-to-left inference form of dfvd2an 37819. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfvd2anir.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
dfvd2anir | ⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfvd2anir.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | dfvd2an 37819 | . 2 ⊢ (( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) ↔ ((𝜑 ∧ 𝜓) → 𝜒)) | |
3 | 1, 2 | mpbir 220 | 1 ⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ( wvd1 37806 ( wvhc2 37817 |
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-vd1 37807 df-vhc2 37818 |
This theorem is referenced by: int3 37858 el021old 37947 el2122old 37965 el12 37974 |
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