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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 40951 | . 2 ⊢ ( 𝜓 ▶ 𝜑 ) |
3 | e01.2 | . 2 ⊢ ( 𝜓 ▶ 𝜒 ) | |
4 | e01.3 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) | |
5 | 2, 3, 4 | e11 41042 | 1 ⊢ ( 𝜓 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd1 40923 |
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-vd1 40924 |
This theorem is referenced by: e01an 41046 trsspwALT 41172 sspwtr 41175 pwtrVD 41178 pwtrrVD 41179 snssiALTVD 41181 snelpwrVD 41185 sstrALT2VD 41188 suctrALT2VD 41190 3impexpVD 41210 ax6e2eqVD 41261 ax6e2ndVD 41262 2sb5ndVD 41264 vk15.4jVD 41268 |
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