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Mirrors > Home > MPE Home > Th. List > r19.43 | Structured version Visualization version Unicode version |
Description: Restricted quantifier version of 19.43 1810. (Contributed by NM, 27-May-1998.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
r19.43 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.35 3084 | . 2 | |
2 | df-or 385 | . . 3 | |
3 | 2 | rexbii 3041 | . 2 |
4 | df-or 385 | . . 3 | |
5 | ralnex 2992 | . . . 4 | |
6 | 5 | imbi1i 339 | . . 3 |
7 | 4, 6 | bitr4i 267 | . 2 |
8 | 1, 3, 7 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wo 383 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-or 385 df-an 386 df-ex 1705 df-ral 2917 df-rex 2918 |
This theorem is referenced by: r19.44v 3094 r19.45v 3095 r19.45zv 4068 r19.44zv 4069 iunun 4604 wemapsolem 8455 pythagtriplem2 15522 pythagtrip 15539 dcubic 24573 legtrid 25486 axcontlem4 25847 erdszelem11 31183 soseq 31751 seglelin 32223 diophun 37337 rexzrexnn0 37368 ldepslinc 42298 |
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