Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  fliftval Unicode version

Theorem fliftval 6214
 Description: The value of the function . (Contributed by Mario Carneiro, 23-Dec-2016.)
Hypotheses
Ref Expression
flift.1
flift.2
flift.3
fliftval.4
fliftval.5
fliftval.6
Assertion
Ref Expression
fliftval
Distinct variable groups:   ,   ,   ,   ,   ,   ,   ,S

Proof of Theorem fliftval
StepHypRef Expression
1 fliftval.6 . . 3
3 simpr 461 . . . 4
4 eqidd 2458 . . . . 5
5 eqidd 2458 . . . . 5
64, 5anim12ci 567 . . . 4
7 fliftval.4 . . . . . . 7
87eqeq2d 2471 . . . . . 6
9 fliftval.5 . . . . . . 7
109eqeq2d 2471 . . . . . 6
118, 10anbi12d 710 . . . . 5
1211rspcev 3210 . . . 4
133, 6, 12syl2anc 661 . . 3
14 flift.1 . . . . 5
15 flift.2 . . . . 5
16 flift.3 . . . . 5
1714, 15, 16fliftel 6207 . . . 4
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E.wrex 2808  <.cop 4035   class class class wbr 4452  e.cmpt 4510  rancrn 5005  Funwfun 5587  `cfv 5593 This theorem is referenced by:  qliftval  7419  cygznlem2  18607  pi1xfrval  21554  pi1coval  21560 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fv 5601