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Mirrors > Home > NFE Home > Th. List > 19.12 | Unicode version |
Description: Theorem 19.12 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! But sometimes the converse does hold, as in 19.12vv 1898 and r19.12sn 3789. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.) |
Ref | Expression |
---|---|
19.12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1788 | . . 3 | |
2 | 1 | nfex 1843 | . 2 |
3 | sp 1747 | . . 3 | |
4 | 3 | eximi 1576 | . 2 |
5 | 2, 4 | alrimi 1765 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wal 1540 wex 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 |
This theorem is referenced by: ax12olem2 1928 |
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