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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 40925 | . . 3 ⊢ (𝜑 → 𝜓) |
3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜒 → 𝜓)) |
4 | 3 | dfvd2ir 40940 | 1 ⊢ ( 𝜑 , 𝜒 ▶ 𝜓 ) |
Colors of variables: wff setvar class |
Syntax hints: ( wvd1 40923 ( wvd2 40931 |
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-vd1 40924 df-vd2 40932 |
This theorem is referenced by: e221 41003 e212 41005 e122 41007 e112 41008 e121 41010 e211 41011 e120 41017 e12 41078 e21 41084 |
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