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Mirrors > Home > MPE Home > Th. List > nexr | Structured version Visualization version GIF version |
Description: Inference associated with the contrapositive of 19.8a 2110. (Contributed by Jeff Hankins, 26-Jul-2009.) |
Ref | Expression |
---|---|
nexr.1 | ⊢ ¬ ∃𝑥𝜑 |
Ref | Expression |
---|---|
nexr | ⊢ ¬ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nexr.1 | . 2 ⊢ ¬ ∃𝑥𝜑 | |
2 | 19.8a 2110 | . 2 ⊢ (𝜑 → ∃𝑥𝜑) | |
3 | 1, 2 | mto 189 | 1 ⊢ ¬ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∃wex 1743 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1759 ax-4 1773 ax-5 1870 ax-6 1929 ax-7 1966 ax-12 2107 |
This theorem depends on definitions: df-bi 199 df-ex 1744 |
This theorem is referenced by: alimp-surprise 44282 |
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