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Mirrors > Home > MPE Home > Th. List > 19.9 | Structured version Visualization version Unicode version |
Description: A wff may be existentially quantified with a variable not free in it. Theorem 19.9 of [Margaris] p. 89. See 19.9v 1896 for a version requiring fewer axioms. (Contributed by FL, 24-Mar-2007.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) Revised to shorten other proofs. (Revised by Wolf Lammen, 14-Jul-2020.) |
Ref | Expression |
---|---|
19.9.1 |
Ref | Expression |
---|---|
19.9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.9.1 | . 2 | |
2 | 19.9t 2071 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wex 1704 wnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nf 1710 |
This theorem is referenced by: exlimd 2087 19.19 2097 19.36 2098 19.41 2103 19.44 2106 19.45 2107 19.9h 2120 exists1 2561 dfid3 5025 fsplit 7282 bnj1189 31077 bj-exexbiex 32691 bj-exalbial 32693 ax6e2ndeq 38775 e2ebind 38779 ax6e2ndeqVD 39145 e2ebindVD 39148 e2ebindALT 39165 ax6e2ndeqALT 39167 |
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