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

Theorem alexeq 3233
 Description: Two ways to express substitution of for in . Obsoleted by alexeqg 3232. (Contributed by NM, 2-Mar-1995.) Obsolete as of 1-May-2019. (New usage is discouraged.)
Hypothesis
Ref Expression
alexeq.1
Assertion
Ref Expression
alexeq
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem alexeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 alexeq.1 . . 3
2 eqeq2 2482 . . . . 5
32anbi1d 704 . . . 4
43exbidv 1690 . . 3
52imbi1d 317 . . . 4
65albidv 1689 . . 3
7 sb56 2154 . . 3
81, 4, 6, 7vtoclb 3168 . 2
98bicomi 202 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1377   wceq 1379  wex 1596   wcel 1767  cvv 3113 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  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-v 3115 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator