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Theorem untbi12d 25125
 Description: Congruence axiom for until. (Contributed by Mario Carneiro, 30-Aug-2016.)
Hypotheses
Ref Expression
untbi12d.1
untbi12d.2
Assertion
Ref Expression
untbi12d

Proof of Theorem untbi12d
StepHypRef Expression
1 untbi12d.1 . . . . 5
21biimpd 198 . . . 4
32untim1d 25123 . . 3
41biimprd 214 . . . 4
54untim1d 25123 . . 3
63, 5impbid 183 . 2
7 untbi12d.2 . . . . 5
87biimpd 198 . . . 4
98untim2d 25124 . . 3
107biimprd 214 . . . 4
1110untim2d 25124 . . 3
129, 11impbid 183 . 2
136, 12bitrd 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wbox 25073   wunt 25076 This theorem is referenced by:  untbi12i  25126  cdequnt  25134 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 25077  ax-ltl2 25078  ax-ltl3 25079  ax-ltl4 25080  ax-lmp 25081  ax-nmp 25082  ax-ltl5 25096  ax-ltl6 25097 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 25083
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