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

Step	Hyp	Ref	Expression
1		fliftval.6	. . 3
2	1	adantr 465	. 2
3		simpr 461	. . . 4
4		eqidd 2458	. . . . 5
5		eqidd 2458	. . . . 5
6	4, 5	anim12ci 567	. . . 4
7		fliftval.4	. . . . . . 7
8	7	eqeq2d 2471	. . . . . 6
9		fliftval.5	. . . . . . 7
10	9	eqeq2d 2471	. . . . . 6
11	8, 10	anbi12d 710	. . . . 5
12	11	rspcev 3210	. . . 4
13	3, 6, 12	syl2anc 661	. . 3
14		flift.1	. . . . 5
15		flift.2	. . . . 5
16		flift.3	. . . . 5
17	14, 15, 16	fliftel 6207	. . . 4
18	17	adantr 465	. . 3
19	13, 18	mpbird 232	. 2
20		funbrfv 5911	. 2
21	2, 19, 20	sylc 60	1

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