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Theorem alexeqd 24962
 Description: Two ways to express substitution of for in . (Contributed by FL, 4-Jun-2012.)
Assertion
Ref Expression
alexeqd
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem alexeqd
StepHypRef Expression
1 elex 2796 . 2
2 eqeq2 2292 . . . . . 6
32imbi1d 308 . . . . 5
43albidv 1611 . . . 4
52anbi1d 685 . . . . 5
65exbidv 1612 . . . 4
74, 6bibi12d 312 . . 3
8 0ex 4150 . . . . 5
98elimel 3617 . . . 4
109alexeq 2897 . . 3
117, 10dedth 3606 . 2
121, 11syl 15 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528   wceq 1623   wcel 1684  cvv 2788  c0 3455  cif 3565 This theorem is referenced by:  intopcoaconb  25540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-nul 4149 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-nul 3456  df-if 3566
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