New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sbralie Unicode version

Theorem sbralie 2848
 Description: Implicit to explicit substitution that swaps variables in a quantified expression. (Contributed by NM, 5-Sep-2004.)
Hypothesis
Ref Expression
sbralie.1
Assertion
Ref Expression
sbralie
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbralie
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvralsv 2846 . . 3
21sbbii 1653 . 2
3 nfv 1619 . . 3
4 raleq 2807 . . 3
53, 4sbie 2038 . 2
6 cbvralsv 2846 . . 3
7 nfv 1619 . . . . . 6
87sbco2 2086 . . . . 5
9 nfv 1619 . . . . . 6
10 sbralie.1 . . . . . . . 8
1110bicomd 192 . . . . . . 7
1211equcoms 1681 . . . . . 6
139, 12sbie 2038 . . . . 5
148, 13bitri 240 . . . 4
1514ralbii 2638 . . 3
166, 15bitri 240 . 2
172, 5, 163bitrri 263 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wsb 1648  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator