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Mirrors > Home > MPE Home > Th. List > Mathboxes > e22 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e22.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e22.2 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
e22.3 | ⊢ (𝜒 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
e22 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e22.1 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | e22.2 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) | |
3 | e22.3 | . . 3 ⊢ (𝜒 → (𝜃 → 𝜏)) | |
4 | 3 | a1i 11 | . 2 ⊢ (𝜒 → (𝜒 → (𝜃 → 𝜏))) |
5 | 1, 1, 2, 4 | e222 40977 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 40918 |
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-vd2 40919 |
This theorem is referenced by: e22an 41013 e02 41038 e12 41065 e20 41068 e21 41071 sspwtr 41162 pwtrVD 41165 pwtrrVD 41166 elex22VD 41180 tpid3gVD 41183 en3lplem2VD 41185 imbi12VD 41214 truniALTVD 41219 trintALTVD 41221 onfrALTlem3VD 41228 onfrALTlem2VD 41230 ax6e2eqVD 41248 ax6e2ndeqVD 41250 sb5ALTVD 41254 |
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