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Mirrors > Home > ILE Home > Th. List > spime | Unicode version |
Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Mar-2018.) |
Ref | Expression |
---|---|
spime.1 | |
spime.2 |
Ref | Expression |
---|---|
spime |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spime.1 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | spime.2 | . . 3 | |
4 | 2, 3 | spimed 1628 | . 2 |
5 | 4 | trud 1252 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wtru 1244 wnf 1349 wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 |
This theorem is referenced by: spimev 1741 |
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