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Mirrors > Home > ILE Home > Th. List > spcev | Unicode version |
Description: Existential specialization, using implicit substitution. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Eric Schmidt, 22-Dec-2006.) |
Ref | Expression |
---|---|
spcv.1 | |
spcv.2 |
Ref | Expression |
---|---|
spcev |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spcv.1 | . 2 | |
2 | spcv.2 | . . 3 | |
3 | 2 | spcegv 2748 | . 2 |
4 | 1, 3 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wex 1453 wcel 1465 cvv 2660 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 |
This theorem is referenced by: bnd2 4067 mss 4118 exss 4119 snnex 4339 opeldm 4712 elrnmpt1 4760 xpmlem 4929 ffoss 5367 ssimaex 5450 fvelrn 5519 eufnfv 5616 foeqcnvco 5659 cnvoprab 6099 domtr 6647 ensn1 6658 ac6sfi 6760 difinfsn 6953 0ct 6960 ctmlemr 6961 ctssdclemn0 6963 ctssdclemr 6965 ctssdc 6966 omct 6970 ctssexmid 6992 exmidfodomrlemim 7025 zfz1iso 10552 ennnfonelemim 11864 ctinfom 11868 ctinf 11870 qnnen 11871 enctlem 11872 ctiunct 11880 subctctexmid 13123 |
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