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Theorem elabgft1 10304
 Description: One implication of elabgf 2708, in closed form. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
elabgf1.nf1
elabgf1.nf2
Assertion
Ref Expression
elabgft1

Proof of Theorem elabgft1
StepHypRef Expression
1 bi1 115 . . . . . 6
2 imim2 53 . . . . . 6
31, 2syl5 32 . . . . 5
43imim2i 12 . . . 4
54alimi 1360 . . 3
6 elabgf1.nf1 . . . 4
7 nfab1 2196 . . . . . 6
86, 7nfel 2202 . . . . 5
9 elabgf1.nf2 . . . . 5
108, 9nfim 1480 . . . 4
11 elabgf0 10303 . . . 4
126, 10, 11bj-vtoclgft 10301 . . 3
135, 12syl 14 . 2
1413pm2.43d 48 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wal 1257   wceq 1259  wnf 1365   wcel 1409  cab 2042  wnfc 2181 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576 This theorem is referenced by:  elabgf1  10305
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