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Mirrors > Home > ILE Home > Th. List > exlimddv | Unicode version |
Description: Existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016.) |
Ref | Expression |
---|---|
exlimddv.1 | |
exlimddv.2 |
Ref | Expression |
---|---|
exlimddv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimddv.1 | . 2 | |
2 | exlimddv.2 | . . . 4 | |
3 | 2 | ex 114 | . . 3 |
4 | 3 | exlimdv 1806 | . 2 |
5 | 1, 4 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1479 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie2 1481 ax-17 1513 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: fvmptdv2 5569 tfrlemi14d 6292 tfrexlem 6293 tfr1onlemres 6308 tfrcllemres 6321 tfrcldm 6322 erref 6512 xpdom2 6788 dom0 6795 xpen 6802 mapdom1g 6804 phplem4dom 6819 phplem4on 6824 fidceq 6826 dif1en 6836 fin0 6842 fin0or 6843 isinfinf 6854 infm 6861 en2eqpr 6864 fiuni 6934 supelti 6958 djudom 7049 difinfsn 7056 enomnilem 7093 enmkvlem 7116 enwomnilem 7124 exmidfodomrlemim 7148 exmidaclem 7155 cc2lem 7198 cc3 7200 genpml 7449 genpmu 7450 ltexprlemm 7532 ltexprlemfl 7541 ltexprlemfu 7543 suplocsr 7741 axpre-suploc 7834 eqord1 8372 nn1suc 8867 seq3f1oleml 10428 zfz1isolem1 10739 nninfdcex 11871 zsupssdc 11872 eulerth 12144 ennnfonelemim 12300 exmidunben 12302 enctlem 12308 ctiunct 12316 unct 12318 omctfn 12319 omiunct 12320 lmff 12796 txcn 12822 suplociccreex 13149 suplociccex 13150 subctctexmid 13722 exmidsbthrlem 13742 sbthom 13746 |
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