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Theorem sbhypf 3081
 Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf 3368. (Contributed by Raph Levien, 10-Apr-2004.)
Hypotheses
Ref Expression
sbhypf.1
sbhypf.2
Assertion
Ref Expression
sbhypf
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem sbhypf
StepHypRef Expression
1 vex 3034 . . 3
2 eqeq1 2475 . . 3
31, 2ceqsexv 3070 . 2
4 nfs1v 2286 . . . 4
5 sbhypf.1 . . . 4
64, 5nfbi 2037 . . 3
7 sbequ12 2098 . . . . 5
87bicomd 206 . . . 4
9 sbhypf.2 . . . 4
108, 9sylan9bb 714 . . 3
116, 10exlimi 2015 . 2
123, 11sylbir 218 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   wceq 1452  wex 1671  wnf 1675  wsb 1805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033 This theorem is referenced by:  mob2  3206  reu2eqd  3223  cbvmptf  4486  ralxpf  4986  tfisi  6704  ac6sf  8937  nn0ind-raph  11058  ac6sf2  28302  nn0min  28459  ac6gf  32123  fdc1  32139
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