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Mirrors > Home > ILE Home > Th. List > r19.2m | Unicode version |
Description: Theorem 19.2 of [Margaris] p. 89 with restricted quantifiers (compare 19.2 1529). The restricted version is valid only when the domain of quantification is inhabited. (Contributed by Jim Kingdon, 5-Aug-2018.) |
Ref | Expression |
---|---|
r19.2m |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2311 | . . . 4 | |
2 | exintr 1525 | . . . 4 | |
3 | 1, 2 | sylbi 114 | . . 3 |
4 | df-rex 2312 | . . 3 | |
5 | 3, 4 | syl6ibr 151 | . 2 |
6 | 5 | impcom 116 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wex 1381 wcel 1393 wral 2306 wrex 2307 |
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-ial 1427 |
This theorem depends on definitions: df-bi 110 df-ral 2311 df-rex 2312 |
This theorem is referenced by: intssunim 3637 riinm 3729 trintssm 3870 iinexgm 3908 xpiindim 4473 cnviinm 4859 eusvobj2 5498 iinerm 6178 r19.2uz 9591 climuni 9814 |
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