Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rexraleqim Structured version   Unicode version

Theorem rexraleqim 3197
 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:   ,,   ,,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rexraleqim
StepHypRef Expression
1 rexraleqim.1 . . . . . . 7
2 eqeq1 2426 . . . . . . 7
31, 2imbi12d 321 . . . . . 6
43rspcva 3180 . . . . 5
5 rexraleqim.2 . . . . . 6
65biimpd 210 . . . . 5
74, 6syli 38 . . . 4
87impancom 441 . . 3
98rexlimiva 2910 . 2
109imp 430 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wcel 1872  wral 2771  wrex 2772 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-v 3082 This theorem is referenced by:  cramerlem3  19713
 Copyright terms: Public domain W3C validator