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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 38787 | . . 3 ⊢ (𝜑 → 𝜓) |
3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜒 → 𝜓)) |
4 | 3 | dfvd2ir 38802 | 1 ⊢ ( 𝜑 , 𝜒 ▶ 𝜓 ) |
Colors of variables: wff setvar class |
Syntax hints: ( wvd1 38785 ( wvd2 38793 |
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 197 df-an 386 df-vd1 38786 df-vd2 38794 |
This theorem is referenced by: e221 38874 e212 38876 e122 38878 e112 38879 e121 38881 e211 38882 e120 38888 e12 38951 e21 38957 |
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