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Theorem sbhypf 2597
 Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf . (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 2554 . . 3
2 eqeq1 2043 . . 3
31, 2ceqsexv 2587 . 2
4 nfs1v 1812 . . . 4
5 sbhypf.1 . . . 4
64, 5nfbi 1478 . . 3
7 sbequ12 1651 . . . . 5
87bicomd 129 . . . 4
9 sbhypf.2 . . . 4
108, 9sylan9bb 435 . . 3
116, 10exlimi 1482 . 2
123, 11sylbir 125 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1242  wnf 1346  wex 1378  wsb 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553 This theorem is referenced by:  mob2  2715  tfisi  4253  ralxpf  4425  rexxpf  4426  nn0ind-raph  8131
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