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Mirrors > Home > MPE Home > Th. List > Mathboxes > e01 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e01.1 | ⊢ 𝜑 |
e01.2 | ⊢ ( 𝜓 ▶ 𝜒 ) |
e01.3 | ⊢ (𝜑 → (𝜒 → 𝜃)) |
Ref | Expression |
---|---|
e01 | ⊢ ( 𝜓 ▶ 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e01.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | vd01 42170 | . 2 ⊢ ( 𝜓 ▶ 𝜑 ) |
3 | e01.2 | . 2 ⊢ ( 𝜓 ▶ 𝜒 ) | |
4 | e01.3 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) | |
5 | 2, 3, 4 | e11 42261 | 1 ⊢ ( 𝜓 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd1 42142 |
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-vd1 42143 |
This theorem is referenced by: e01an 42265 trsspwALT 42391 sspwtr 42394 pwtrVD 42397 pwtrrVD 42398 snssiALTVD 42400 snelpwrVD 42404 sstrALT2VD 42407 suctrALT2VD 42409 3impexpVD 42429 ax6e2eqVD 42480 ax6e2ndVD 42481 2sb5ndVD 42483 vk15.4jVD 42487 |
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