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Theorem sbhypf 2904
 Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf 3171. (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 2862 . . 3
2 eqeq1 2359 . . 3
31, 2ceqsexv 2894 . 2
4 nfs1v 2106 . . . 4
5 sbhypf.1 . . . 4
64, 5nfbi 1834 . . 3
7 sbequ12 1919 . . . . 5
87bicomd 192 . . . 4
9 sbhypf.2 . . . 4
108, 9sylan9bb 680 . . 3
116, 10exlimi 1803 . 2
123, 11sylbir 204 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541  wnf 1544   wceq 1642  wsb 1648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  mob2  3016  ralxpf  4827
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