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Mirrors > Home > NFE Home > Th. List > rexcom13 | Unicode version |
Description: Swap 1st and 3rd restricted existential quantifiers. (Contributed by NM, 8-Apr-2015.) |
Ref | Expression |
---|---|
rexcom13 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom 2772 | . 2 | |
2 | rexcom 2772 | . . 3 | |
3 | 2 | rexbii 2639 | . 2 |
4 | rexcom 2772 | . 2 | |
5 | 1, 3, 4 | 3bitri 262 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wrex 2615 |
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 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 |
This theorem is referenced by: rexrot4 2774 |
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