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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 1631). The restricted version is valid only when the domain of quantification is inhabited. (Contributed by Jim Kingdon, 5-Aug-2018.) (Revised by Jim Kingdon, 7-Apr-2023.) |
Ref | Expression |
---|---|
r19.2m |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1w 2231 | . . . 4 | |
2 | 1 | cbvexv 1911 | . . 3 |
3 | eleq1w 2231 | . . . 4 | |
4 | 3 | cbvexv 1911 | . . 3 |
5 | 2, 4 | bitri 183 | . 2 |
6 | df-ral 2453 | . . . . 5 | |
7 | exintr 1627 | . . . . 5 | |
8 | 6, 7 | sylbi 120 | . . . 4 |
9 | df-rex 2454 | . . . 4 | |
10 | 8, 9 | syl6ibr 161 | . . 3 |
11 | 10 | impcom 124 | . 2 |
12 | 5, 11 | sylanbr 283 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wex 1485 wcel 2141 wral 2448 wrex 2449 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 df-clel 2166 df-ral 2453 df-rex 2454 |
This theorem is referenced by: intssunim 3851 riinm 3943 iinexgm 4138 xpiindim 4746 cnviinm 5150 eusvobj2 5837 iinerm 6582 suplocexprlemml 7667 rexfiuz 10942 r19.2uz 10946 climuni 11245 pc2dvds 12272 cncnp2m 12986 |
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