**Description:** First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

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

Hypothesis | bnj1299.1 | $${\u22a2}{\phi}\to \exists {x}\in {A}\phantom{\rule{.4em}{0ex}}\left({\psi}\wedge {\chi}\right)$$ | |

Assertion | bnj1299 | $${\u22a2}{\phi}\to \exists {x}\in {A}\phantom{\rule{.4em}{0ex}}{\psi}$$ |

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

1 | bnj1299.1 | $${\u22a2}{\phi}\to \exists {x}\in {A}\phantom{\rule{.4em}{0ex}}\left({\psi}\wedge {\chi}\right)$$ | |

2 | bnj1239 | $${\u22a2}\exists {x}\in {A}\phantom{\rule{.4em}{0ex}}\left({\psi}\wedge {\chi}\right)\to \exists {x}\in {A}\phantom{\rule{.4em}{0ex}}{\psi}$$ | |

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