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

Theorem mosub 3277
Description: "At most one" remains true after substitution. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
mosub.1
Assertion
Ref Expression
mosub
Distinct variable group:   , ,

Proof of Theorem mosub
StepHypRef Expression
1 moeq 3275 . 2
2 mosub.1 . . 3
32ax-gen 1618 . 2
4 moexexv 2364 . 2
51, 3, 4mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  E*wmo 2283
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  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
  Copyright terms: Public domain W3C validator