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Mirrors > Home > NFE Home > Th. List > simprll | GIF version |
Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.) |
Ref | Expression |
---|---|
simprll | ⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 443 | . 2 ⊢ ((ψ ∧ χ) → ψ) | |
2 | 1 | ad2antrl 708 | 1 ⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → ψ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: nnsucelr 4428 nnpw1ex 4484 sfin112 4529 sfinltfin 4535 enprmaplem3 6078 |
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