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Mirrors > Home > NFE Home > Th. List > simp2lr | GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp2lr | ⊢ ((θ ∧ ((φ ∧ ψ) ∧ χ) ∧ τ) → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simplr 731 | . 2 ⊢ (((φ ∧ ψ) ∧ χ) → ψ) | |
2 | 1 | 3ad2ant2 977 | 1 ⊢ ((θ ∧ ((φ ∧ ψ) ∧ χ) ∧ τ) → ψ) |
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: nnpweq 4523 sfin112 4529 |
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