Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  3sstr3i Unicode version

Theorem 3sstr3i 3229
 Description: Substitution of equality in both sides of a subclass relationship. (Contributed by NM, 13-Jan-1996.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
3sstr3.1
3sstr3.2
3sstr3.3
Assertion
Ref Expression
3sstr3i

Proof of Theorem 3sstr3i
StepHypRef Expression
1 3sstr3.1 . 2
2 3sstr3.2 . . 3
3 3sstr3.3 . . 3
42, 3sseq12i 3217 . 2
51, 4mpbi 199 1
 Colors of variables: wff set class Syntax hints:   wceq 1632   wss 3165 This theorem is referenced by:  odf1o2  14900  leordtval2  16958  uniiccvol  18951 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179
 Copyright terms: Public domain W3C validator