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Theorem axgroth5 8700
 Description: The Tarski-Grothendieck axiom using abbreviations. (Contributed by NM, 22-Jun-2009.)
Assertion
Ref Expression
axgroth5
Distinct variable group:   ,,,

Proof of Theorem axgroth5
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-groth 8699 . 2
2 biid 229 . . . 4
3 pwss 3814 . . . . . 6
4 pwss 3814 . . . . . . 7
54rexbii 2731 . . . . . 6
63, 5anbi12i 680 . . . . 5
76ralbii 2730 . . . 4
8 df-ral 2711 . . . . 5
9 vex 2960 . . . . . . . 8
109elpw 3806 . . . . . . 7
1110imbi1i 317 . . . . . 6
1211albii 1576 . . . . 5
138, 12bitri 242 . . . 4
142, 7, 133anbi123i 1143 . . 3
1514exbii 1593 . 2
161, 15mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360   w3a 937  wal 1550  wex 1551   wcel 1726  wral 2706  wrex 2707   wss 3321  cpw 3800   class class class wbr 4213   cen 7107 This theorem is referenced by:  grothpw  8702  grothpwex  8703  axgroth6  8704  grothtsk  8711 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-groth 8699 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-v 2959  df-in 3328  df-ss 3335  df-pw 3802
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