New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > sylnibr | GIF version |
Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by Wolf Lammen, 16-Dec-2013.) |
Ref | Expression |
---|---|
sylnibr.1 | ⊢ (φ → ¬ ψ) |
sylnibr.2 | ⊢ (χ ↔ ψ) |
Ref | Expression |
---|---|
sylnibr | ⊢ (φ → ¬ χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylnibr.1 | . 2 ⊢ (φ → ¬ ψ) | |
2 | sylnibr.2 | . . 3 ⊢ (χ ↔ ψ) | |
3 | 2 | bicomi 193 | . 2 ⊢ (ψ ↔ χ) |
4 | 1, 3 | sylnib 295 | 1 ⊢ (φ → ¬ χ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 176 |
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 |
This theorem is referenced by: ncfinraise 4481 tfinltfin 4501 sfindbl 4530 tfinnn 4534 vfinncvntsp 4549 nnc3n3p1 6276 nnc3n3p2 6277 nnc3p1n3p2 6278 nchoicelem2 6288 |
Copyright terms: Public domain | W3C validator |