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Theorem r2exlem 2977
Description: Lemma factoring out common proof steps in r2exf 2978 an r2ex 2980. Introduced to reduce dependencies on axioms. (Contributed by Wolf Lammen, 10-Jan-2020.)
Hypothesis
Ref Expression
r2exlem.1
Assertion
Ref Expression
r2exlem

Proof of Theorem r2exlem
StepHypRef Expression
1 exnal 1648 . . 3
2 r2exlem.1 . . 3
31, 2xchbinxr 311 . 2
4 alinexa 1663 . . . 4
54con2bii 332 . . 3
65exbii 1667 . 2
7 ralnex 2903 . . . . 5
87ralbii 2888 . . . 4
9 ralnex 2903 . . . 4
108, 9bitri 249 . . 3
1110con2bii 332 . 2
123, 6, 113bitr4ri 278 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  A.wral 2807  E.wrex 2808
This theorem is referenced by:  r2exf  2978  r2ex  2980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-ral 2812  df-rex 2813
  Copyright terms: Public domain W3C validator