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Mirrors > Home > NFE Home > Th. List > ancld | GIF version |
Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.) |
Ref | Expression |
---|---|
ancld.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
ancld | ⊢ (φ → (ψ → (ψ ∧ χ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 21 | . 2 ⊢ (φ → (ψ → ψ)) | |
2 | ancld.1 | . 2 ⊢ (φ → (ψ → χ)) | |
3 | 1, 2 | jcad 519 | 1 ⊢ (φ → (ψ → (ψ ∧ χ))) |
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: mopick2 2271 cgsexg 2890 cgsex2g 2891 cgsex4g 2892 reximdva0 3561 difsn 3845 preq12b 4127 nnpw1ex 4484 tfin11 4493 vinf 4555 dmcosseq 4973 ssreseq 4997 fnoprabg 5585 dmfrec 6314 |
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