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Mirrors > Home > MPE Home > Th. List > Mathboxes > vd02 | Structured version Visualization version GIF version |
Description: Two virtual hypotheses virtually infer a theorem. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vd02.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
vd02 | ⊢ ( 𝜓 , 𝜒 ▶ 𝜑 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vd02.1 | . . . 4 ⊢ 𝜑 | |
2 | 1 | a1i 11 | . . 3 ⊢ (𝜒 → 𝜑) |
3 | 2 | a1i 11 | . 2 ⊢ (𝜓 → (𝜒 → 𝜑)) |
4 | 3 | dfvd2ir 42206 | 1 ⊢ ( 𝜓 , 𝜒 ▶ 𝜑 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 42197 |
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 206 df-an 397 df-vd2 42198 |
This theorem is referenced by: e220 42257 e202 42259 e022 42261 e002 42263 e020 42265 e200 42267 e02 42317 e20 42347 |
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