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Theorem axgroth5 9223
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 9222 . 2
2 biid 236 . . . 4
3 pwss 4027 . . . . . 6
4 pwss 4027 . . . . . . 7
54rexbii 2959 . . . . . 6
63, 5anbi12i 697 . . . . 5
76ralbii 2888 . . . 4
8 df-ral 2812 . . . . 5
9 selpw 4019 . . . . . . 7
109imbi1i 325 . . . . . 6
1110albii 1640 . . . . 5
128, 11bitri 249 . . . 4
132, 7, 123anbi123i 1185 . . 3
1413exbii 1667 . 2
151, 14mpbir 209 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  \/wo 368  /\wa 369  /\w3a 973  A.wal 1393  E.wex 1612  e.wcel 1818  A.wral 2807  E.wrex 2808  C_wss 3475  ~Pcpw 4012   class class class wbr 4452   cen 7533
This theorem is referenced by:  grothpw  9225  grothpwex  9226  axgroth6  9227  grothtsk  9234
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  ax-groth 9222
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  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  df-in 3482  df-ss 3489  df-pw 4014
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