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Theorem r2exlem 2909
 Description: Lemma factoring out common proof steps in r2exf 2910 an r2ex 2912. 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 1698 . . 3
2 r2exlem.1 . . 3
31, 2xchbinxr 313 . 2
4 alinexa 1712 . . . 4
54con2bii 334 . . 3
65exbii 1717 . 2
7 ralnex 2833 . . . . 5
87ralbii 2818 . . . 4
9 ralnex 2833 . . . 4
108, 9bitri 253 . . 3
1110con2bii 334 . 2
123, 6, 113bitr4ri 282 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1441  wex 1662   wcel 1886  wral 2736  wrex 2737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-ral 2741  df-rex 2742 This theorem is referenced by:  r2exf  2910  r2ex  2912
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