New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > ancrd | GIF version |
Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.) |
Ref | Expression |
---|---|
ancrd.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
ancrd | ⊢ (φ → (ψ → (χ ∧ ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancrd.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | idd 21 | . 2 ⊢ (φ → (ψ → ψ)) | |
3 | 1, 2 | jcad 519 | 1 ⊢ (φ → (ψ → (χ ∧ ψ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 |
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 |
This theorem is referenced by: impac 604 euan 2261 2eu1 2284 reupick 3539 spfininduct 4540 vinf 4555 ssrnres 5059 funssres 5144 dffo4 5423 dffo5 5424 |
Copyright terms: Public domain | W3C validator |