Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sb5rf Structured version   Unicode version

Theorem sb5rf 2165
 Description: Reversed substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sb5rf.1
Assertion
Ref Expression
sb5rf

Proof of Theorem sb5rf
StepHypRef Expression
1 sb5rf.1 . . . 4
21sbid2 2159 . . 3
3 sb1 1662 . . 3
42, 3sylbir 205 . 2
5 stdpc7 1942 . . . 4
65imp 419 . . 3
71, 6exlimi 1821 . 2
84, 7impbii 181 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550  wnf 1553  wsb 1658 This theorem is referenced by:  2sb5rf  2193 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
 Copyright terms: Public domain W3C validator