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Mirrors > Home > NFE Home > Th. List > syl3anl1 | GIF version |
Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.) |
Ref | Expression |
---|---|
syl3anl1.1 | ⊢ (φ → ψ) |
syl3anl1.2 | ⊢ (((ψ ∧ χ ∧ θ) ∧ τ) → η) |
Ref | Expression |
---|---|
syl3anl1 | ⊢ (((φ ∧ χ ∧ θ) ∧ τ) → η) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl3anl1.1 | . . 3 ⊢ (φ → ψ) | |
2 | 1 | 3anim1i 1138 | . 2 ⊢ ((φ ∧ χ ∧ θ) → (ψ ∧ χ ∧ θ)) |
3 | syl3anl1.2 | . 2 ⊢ (((ψ ∧ χ ∧ θ) ∧ τ) → η) | |
4 | 2, 3 | sylan 457 | 1 ⊢ (((φ ∧ χ ∧ θ) ∧ τ) → η) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 ∧ w3a 934 |
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 177 df-an 360 df-3an 936 |
This theorem is referenced by: (None) |
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