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Mirrors > Home > MPE Home > Th. List > mp3an2ani | Structured version Visualization version GIF version |
Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.) |
Ref | Expression |
---|---|
mp3an2ani.1 | ⊢ 𝜑 |
mp3an2ani.2 | ⊢ (𝜓 → 𝜒) |
mp3an2ani.3 | ⊢ ((𝜓 ∧ 𝜃) → 𝜏) |
mp3an2ani.4 | ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
mp3an2ani | ⊢ ((𝜓 ∧ 𝜃) → 𝜂) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp3an2ani.1 | . . 3 ⊢ 𝜑 | |
2 | mp3an2ani.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
3 | mp3an2ani.3 | . . 3 ⊢ ((𝜓 ∧ 𝜃) → 𝜏) | |
4 | mp3an2ani.4 | . . 3 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜏) → 𝜂) | |
5 | 1, 2, 3, 4 | mp3an3an 1430 | . 2 ⊢ ((𝜓 ∧ (𝜓 ∧ 𝜃)) → 𝜂) |
6 | 5 | anabss5 857 | 1 ⊢ ((𝜓 ∧ 𝜃) → 𝜂) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 ∧ w3a 1037 |
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 197 df-an 386 df-3an 1039 |
This theorem is referenced by: 2lgsoddprmlem2 25134 isosctrlem1ALT 39170 odz2prm2pw 41475 lighneallem4 41527 |
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