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

Theorem sbhypf 3156
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf 3453. (Contributed by Raph Levien, 10-Apr-2004.)
Hypotheses
Ref Expression
sbhypf.1
sbhypf.2
Assertion
Ref Expression
sbhypf
Distinct variable groups:   ,   ,

Proof of Theorem sbhypf
StepHypRef Expression
1 vex 3112 . . 3
2 eqeq1 2461 . . 3
31, 2ceqsexv 3146 . 2
4 nfs1v 2181 . . . 4
5 sbhypf.1 . . . 4
64, 5nfbi 1934 . . 3
7 sbequ12 1992 . . . . 5
87bicomd 201 . . . 4
9 sbhypf.2 . . . 4
108, 9sylan9bb 699 . . 3
116, 10exlimi 1912 . 2
123, 11sylbir 213 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  [wsb 1739
This theorem is referenced by:  mob2  3279  reu2eqd  3296  ralxpf  5154  tfisi  6693  ac6sf  8890  nn0ind-raph  10989  cbvmptf  27494  nn0min  27611  ac6gf  30223  fdc1  30239
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-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
  Copyright terms: Public domain W3C validator