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Theorem rexraleqim 3225
Description: Statement following from existence and generalization with equality. (Contributed by AV, 9-Feb-2019.)
Hypotheses
Ref Expression
rexraleqim.1
rexraleqim.2
Assertion
Ref Expression
rexraleqim
Distinct variable groups:   , ,   , ,   ,   ,   ,

Proof of Theorem rexraleqim
StepHypRef Expression
1 rexraleqim.1 . . . . . . 7
2 eqeq1 2461 . . . . . . 7
31, 2imbi12d 320 . . . . . 6
43rspcva 3208 . . . . 5
5 rexraleqim.2 . . . . . 6
65biimpd 207 . . . . 5
74, 6syli 37 . . . 4
87impancom 440 . . 3
98rexlimiva 2945 . 2
109imp 429 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808
This theorem is referenced by:  cramerlem3  19191
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111
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