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| Mirrors > Home > MPE Home > Th. List > Mathboxes > vd12 | Structured version Visualization version GIF version | ||
| Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and an additional hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| vd12.1 | ⊢ ( 𝜑 ▶ 𝜓 ) | 
| Ref | Expression | 
|---|---|
| vd12 | ⊢ ( 𝜑 , 𝜒 ▶ 𝜓 ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | vd12.1 | . . . 4 ⊢ ( 𝜑 ▶ 𝜓 ) | |
| 2 | 1 | in1 44591 | . . 3 ⊢ (𝜑 → 𝜓) | 
| 3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜒 → 𝜓)) | 
| 4 | 3 | dfvd2ir 44606 | 1 ⊢ ( 𝜑 , 𝜒 ▶ 𝜓 ) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ( wvd1 44589 ( wvd2 44597 | 
| 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 207 df-an 396 df-vd1 44590 df-vd2 44598 | 
| This theorem is referenced by: e221 44669 e212 44671 e122 44673 e112 44674 e121 44676 e211 44677 e120 44683 e12 44744 e21 44750 | 
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