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Mirrors > Home > MPE Home > Th. List > mp3anr1 | Structured version Visualization version GIF version |
Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006.) |
Ref | Expression |
---|---|
mp3anr1.1 | ⊢ 𝜓 |
mp3anr1.2 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏) |
Ref | Expression |
---|---|
mp3anr1 | ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜃)) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp3anr1.1 | . . 3 ⊢ 𝜓 | |
2 | mp3anr1.2 | . . . 4 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏) | |
3 | 2 | ancoms 459 | . . 3 ⊢ (((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑) → 𝜏) |
4 | 1, 3 | mp3anl1 1455 | . 2 ⊢ (((𝜒 ∧ 𝜃) ∧ 𝜑) → 𝜏) |
5 | 4 | ancoms 459 | 1 ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜃)) → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1087 |
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 397 df-3an 1089 |
This theorem is referenced by: vc2OLD 29684 vc0 29690 vcm 29692 nvaddsub4 29773 nvpi 29783 nvge0 29789 ipval3 29825 ipidsq 29826 lnoadd 29874 lnosub 29875 dipsubdir 29964 finorwe 36065 |
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