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Theorem axprimlem1 3190
Description: Lemma for the primitive axioms. Primitive form of equality to a singleton.
Assertion
Ref Expression
axprimlem1
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem axprimlem1
StepHypRef Expression
1 dfcleq 1889 . 2
2 vex 2303 . . . . 5
32elsn 2836 . . . 4
43bibi2i 301 . . 3
54albii 1342 . 2
61, 5bitri 237 1
Colors of variables: wff set class
Syntax hints:   wb 173  wal 1322   wceq 1398   wcel 1400  csn 2803
This theorem is referenced by:  axprimlem2  3191  axsiprim  3195  axtyplowerprim  3196  axins2prim  3197  axins3prim  3198
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1323  ax-6 1324  ax-7 1325  ax-gen 1326  ax-8 1402  ax-10 1403  ax-11 1404  ax-12 1405  ax-17 1413  ax-9 1424  ax-4 1429  ax-16 1606  ax-ext 1877
This theorem depends on definitions:  df-bi 174  df-or 356  df-an 357  df-ex 1328  df-sb 1568  df-clab 1883  df-cleq 1888  df-clel 1891  df-v 2302  df-sn 2807
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