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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > e21 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule (see syl6ci 71). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e21.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e21.2 | ⊢ ( 𝜑 ▶ 𝜃 ) |
e21.3 | ⊢ (𝜒 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
e21 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e21.1 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | e21.2 | . . 3 ⊢ ( 𝜑 ▶ 𝜃 ) | |
3 | 2 | vd12 43850 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
4 | e21.3 | . 2 ⊢ (𝜒 → (𝜃 → 𝜏)) | |
5 | 1, 3, 4 | e22 43921 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd1 43819 ( wvd2 43827 |
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 396 df-vd1 43820 df-vd2 43828 |
This theorem is referenced by: e21an 43981 en3lplem1VD 44093 exbiriVD 44104 syl5impVD 44113 sbcim2gVD 44125 onfrALTlem3VD 44137 onfrALTlem2VD 44139 hbimpgVD 44154 ax6e2eqVD 44157 vk15.4jVD 44164 |
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