Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-rspgt Unicode version

Theorem bj-rspgt 13306
 Description: Restricted specialization, generalized. Weakens a hypothesis of rspccv 2810 and seems to have a shorter proof. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
bj-rspg.nfa
bj-rspg.nfb
bj-rspg.nf2
Assertion
Ref Expression
bj-rspgt

Proof of Theorem bj-rspgt
StepHypRef Expression
1 eleq1 2217 . . . . . . . . 9
21imbi1d 230 . . . . . . . 8
32biimpd 143 . . . . . . 7
4 imim2 55 . . . . . . . 8
54imim2d 54 . . . . . . 7
63, 5syl9 72 . . . . . 6
76a2i 11 . . . . 5
87alimi 1432 . . . 4
9 bj-rspg.nfa . . . . 5
10 bj-rspg.nfb . . . . . . 7
119, 10nfel 2305 . . . . . 6
12 nfra1 2485 . . . . . . 7
13 bj-rspg.nf2 . . . . . . 7
1412, 13nfim 1549 . . . . . 6
1511, 14nfim 1549 . . . . 5
16 rsp 2501 . . . . . . 7
1716a1i 9 . . . . . 6
1817com23 78 . . . . 5
199, 15, 18bj-vtoclgft 13295 . . . 4
208, 19syl 14 . . 3
2120pm2.43d 50 . 2
2221com23 78 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1330   wceq 1332  wnf 1437   wcel 2125  wnfc 2283  wral 2432 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-v 2711 This theorem is referenced by:  bj-rspg  13307
 Copyright terms: Public domain W3C validator