Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sb5ALT Structured version   Unicode version

Theorem sb5ALT 32392
 Description: Equivalence for substitution. Alternate proof of sb5 2157. This proof is sb5ALTVD 32811 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sb5ALT
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb5ALT
StepHypRef Expression
1 equsb1 2080 . . . 4
2 sban 2114 . . . . 5
32simplbi2com 627 . . . 4
41, 3mpi 17 . . 3
5 spsbe 1715 . . 3
64, 5syl 16 . 2
7 hbs1 2163 . . 3
8 simpr 461 . . . . 5
98a1i 11 . . . 4
10 simpl 457 . . . . 5
1110a1i 11 . . . 4
12 sbequ1 1960 . . . . 5
1312com12 31 . . . 4
149, 11, 13syl6c 64 . . 3
157, 14exlimexi 32391 . 2
166, 15impbii 188 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wex 1596  wsb 1711 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803  ax-13 1968 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1597  df-nf 1600  df-sb 1712 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator