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Mirrors > Home > MPE Home > Th. List > dfral2 | Structured version Visualization version Unicode version |
Description: Relationship between restricted universal and existential quantifiers. (Contributed by NM, 21-Jan-1997.) Allow shortening of rexnal 2995. (Revised by Wolf Lammen, 9-Dec-2019.) |
Ref | Expression |
---|---|
dfral2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotb 304 | . . 3 | |
2 | 1 | ralbii 2980 | . 2 |
3 | ralnex 2992 | . 2 | |
4 | 2, 3 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wral 2912 wrex 2913 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-ral 2917 df-rex 2918 |
This theorem is referenced by: rexnal 2995 boxcutc 7951 infssuni 8257 ac6n 9307 indstr 11756 trfil3 21692 tglowdim2ln 25546 nmobndseqi 27634 stri 29116 hstri 29124 reprinfz1 30700 bnj1204 31080 nosepon 31818 poimirlem1 33410 n0elqs 34098 |
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