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Mirrors > Home > MPE Home > Th. List > Mathboxes > e23 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule (see syl10 79). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e23.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e23.2 | ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜏 ) |
e23.3 | ⊢ (𝜒 → (𝜏 → 𝜂)) |
Ref | Expression |
---|---|
e23 | ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e23.1 | . . 3 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | 1 | vd23 41836 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜒 ) |
3 | e23.2 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜏 ) | |
4 | e23.3 | . 2 ⊢ (𝜒 → (𝜏 → 𝜂)) | |
5 | 2, 3, 4 | e33 41968 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 41811 ( wvd3 41821 |
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 210 df-an 400 df-3an 1091 df-vd2 41812 df-vd3 41824 |
This theorem is referenced by: e23an 41990 suctrALT2VD 42070 rspsbc2VD 42089 tratrbVD 42095 imbi12VD 42107 imbi13VD 42108 |
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