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Theorem cdequnt 25031
 Description: Distribute conditional equality over 'until'. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
cdeqbox.1 CondEq
cdequnt.2 CondEq
Assertion
Ref Expression
cdequnt CondEq

Proof of Theorem cdequnt
StepHypRef Expression
1 ax-lll 25027 . . 3
2 alneal1 25000 . . . . 5
3 cdeqbox.1 . . . . . 6 CondEq
43cdeqri 2977 . . . . 5
52, 4syl 15 . . . 4
6 cdequnt.2 . . . . . 6 CondEq
76cdeqri 2977 . . . . 5
82, 7syl 15 . . . 4
95, 8untbi12d 25022 . . 3
101, 9syl 15 . 2
1110cdeqi 2976 1 CondEq
 Colors of variables: wff set class Syntax hints:   wb 176   wceq 1623  CondEqwcdeq 2974  wbox 24970   wunt 24973 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 24974  ax-ltl2 24975  ax-ltl3 24976  ax-ltl4 24977  ax-lmp 24978  ax-nmp 24979  ax-ltl5 24993  ax-ltl6 24994  ax-lll 25027 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-cdeq 2975  df-dia 24980
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