Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  2sb6rf Unicode version

Theorem 2sb6rf 2196
 Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.) Remove variable constraints. (Revised by Wolf Lammen, 28-Sep-2018.)
Hypotheses
Ref Expression
2sb5rf.1
2sb5rf.2
Assertion
Ref Expression
2sb6rf
Distinct variable group:   ,

Proof of Theorem 2sb6rf
StepHypRef Expression
1 sbequ12r 1993 . . . . 5
2 sbequ12r 1993 . . . . 5
31, 2sylan9bb 699 . . . 4
43pm5.74i 245 . . 3
542albii 1641 . 2
6 2sb5rf.2 . . . . 5
7619.23 1910 . . . 4
87albii 1640 . . 3
9 2sb5rf.1 . . . 4
10919.23 1910 . . 3
118, 10bitri 249 . 2
12 2ax6e 2194 . . 3
13 pm5.5 336 . . 3
1412, 13ax-mp 5 . 2
155, 11, 143bitrri 272 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  [wsb 1739 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
 Copyright terms: Public domain W3C validator