**Description:** Inference adding existential quantifier to antecedent and consequent.
(Contributed by NM, 10-Jan-1993)

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

Hypothesis | eximi.1 | $${\u22a2}{\phi}\to {\psi}$$ | |

Assertion | eximi | $${\u22a2}\exists {x}\phantom{\rule{.4em}{0ex}}{\phi}\to \exists {x}\phantom{\rule{.4em}{0ex}}{\psi}$$ |

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

1 | eximi.1 | $${\u22a2}{\phi}\to {\psi}$$ | |

2 | exim | $${\u22a2}\forall {x}\phantom{\rule{.4em}{0ex}}\left({\phi}\to {\psi}\right)\to \left(\exists {x}\phantom{\rule{.4em}{0ex}}{\phi}\to \exists {x}\phantom{\rule{.4em}{0ex}}{\psi}\right)$$ | |

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