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Mirrors > Home > NFE Home > Th. List > r19.2z | Unicode version |
Description: Theorem 19.2 of [Margaris] p. 89 with restricted quantifiers (compare 19.2 1659). The restricted version is valid only when the domain of quantification is not empty. (Contributed by NM, 15-Nov-2003.) |
Ref | Expression |
---|---|
r19.2z |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2619 | . . . 4 | |
2 | exintr 1614 | . . . 4 | |
3 | 1, 2 | sylbi 187 | . . 3 |
4 | n0 3559 | . . 3 | |
5 | df-rex 2620 | . . 3 | |
6 | 3, 4, 5 | 3imtr4g 261 | . 2 |
7 | 6 | impcom 419 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wal 1540 wex 1541 wcel 1710 wne 2516 wral 2614 wrex 2615 c0 3550 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-nul 3551 |
This theorem is referenced by: r19.2zb 3640 intssuni 3948 riinn0 4040 |
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