Mathbox for Wolf Lammen < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-sbcom3 Structured version   Unicode version

Theorem wl-sbcom3 30197
 Description: Substituting for and then for is equivalent to substituting for both and . Copy of ~? sbcom3OLD with a shortened proof. Keep this theorem for a while here because an external reference to it exists. (Contributed by Giovanni Mascellani, 8-Apr-2018.) (Proof shortened by Wolf Lammen, 15-Sep-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
wl-sbcom3

Proof of Theorem wl-sbcom3
StepHypRef Expression
1 nfa1 1898 . . . 4
2 sbequ 2118 . . . . 5
32sps 1866 . . . 4
41, 3sbbid 2145 . . 3
52pm5.74i 245 . . . . . 6
65albii 1641 . . . . 5
76a1i 11 . . . 4
8 sb4b 2099 . . . 4
9 sb4b 2099 . . . 4
107, 8, 93bitr4d 285 . . 3
114, 10pm2.61i 164 . 2
12 sbcom 2162 . 2
1311, 12bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184  wal 1393  wsb 1740 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1614  df-nf 1618  df-sb 1741 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator