**Description:** Deduction associated with nfnt . (Contributed by Mario Carneiro, 24-Sep-2016)

Ref | Expression | ||
---|---|---|---|

Hypothesis | nfnd.1 | $${\u22a2}{\phi}\to \u2132{x}\phantom{\rule{.4em}{0ex}}{\psi}$$ | |

Assertion | nfnd | $${\u22a2}{\phi}\to \u2132{x}\phantom{\rule{.4em}{0ex}}\neg {\psi}$$ |

Step | Hyp | Ref | Expression |
---|---|---|---|

1 | nfnd.1 | $${\u22a2}{\phi}\to \u2132{x}\phantom{\rule{.4em}{0ex}}{\psi}$$ | |

2 | nfnt | $${\u22a2}\u2132{x}\phantom{\rule{.4em}{0ex}}{\psi}\to \u2132{x}\phantom{\rule{.4em}{0ex}}\neg {\psi}$$ | |

3 | 1 2 | syl | $${\u22a2}{\phi}\to \u2132{x}\phantom{\rule{.4em}{0ex}}\neg {\psi}$$ |