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Mirrors > Home > ILE Home > Th. List > mp3anr1 | 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 264 | . . 3 ⊢ (((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑) → 𝜏) |
4 | 1, 3 | mp3anl1 1262 | . 2 ⊢ (((𝜒 ∧ 𝜃) ∧ 𝜑) → 𝜏) |
5 | 4 | ancoms 264 | 1 ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜃)) → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |