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Theorem reu7 3031
 Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.)
Hypothesis
Ref Expression
rmo4.1
Assertion
Ref Expression
reu7
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reu7
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 reu3 3026 . 2
2 rmo4.1 . . . . . . 7
3 eqeq1 2359 . . . . . . . 8
4 eqcom 2355 . . . . . . . 8
53, 4syl6bb 252 . . . . . . 7
62, 5imbi12d 311 . . . . . 6
76cbvralv 2835 . . . . 5
87rexbii 2639 . . . 4
9 eqeq1 2359 . . . . . . 7
109imbi2d 307 . . . . . 6
1110ralbidv 2634 . . . . 5
1211cbvrexv 2836 . . . 4
138, 12bitri 240 . . 3
1413anbi2i 675 . 2
151, 14bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642  wral 2614  wrex 2615  wreu 2616 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-reu 2621  df-rmo 2622 This theorem is referenced by: (None)
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