**Description:** Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996)

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

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

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

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

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

2 | 1 | a1i | $${\u22a2}{x}\in {A}\to \left({\phi}\to {\psi}\right)$$ |

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