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Mirrors > Home > MPE Home > Th. List > Mathboxes > iden2 | Structured version Visualization version GIF version |
Description: Virtual deduction identity rule. simpr 476 in conjunction form Virtual Deduction notation. (Contributed by Alan Sare, 5-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
iden2 | ⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 476 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | dfvd2an 37819 | . 2 ⊢ (( ( 𝜑 , 𝜓 ) ▶ 𝜓 ) ↔ ((𝜑 ∧ 𝜓) → 𝜓)) | |
3 | 1, 2 | mpbir 220 | 1 ⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜓 ) |
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-an 385 df-vd1 37807 df-vhc2 37818 |
This theorem is referenced by: (None) |
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