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Theorem r2allem 2832
Description: Lemma factoring out common proof steps of r2alf 2833 and r2al 2835. Introduced to reduce dependencies on axioms. (Contributed by Wolf Lammen, 9-Jan-2020.)
Hypothesis
Ref Expression
r2allem.1
Assertion
Ref Expression
r2allem

Proof of Theorem r2allem
StepHypRef Expression
1 df-ral 2812 . 2
2 r2allem.1 . . . 4
3 impexp 446 . . . . 5
43albii 1640 . . . 4
5 df-ral 2812 . . . . 5
65imbi2i 312 . . . 4
72, 4, 63bitr4i 277 . . 3
87albii 1640 . 2
91, 8bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  A.wral 2807
This theorem is referenced by:  r2alf  2833  r2al  2835
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-ral 2812
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