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Theorem albineal 25102
 Description: always holds iff holds in the first step and always holds in the next step. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
albineal

Proof of Theorem albineal
StepHypRef Expression
1 boxeq 25090 . 2
2 evpexun 25101 . . . 4
3 ax-ltl5 25096 . . . 4
42, 3bitri 240 . . 3
54notbii 287 . 2
6 ioran 476 . . 3
7 notnot 282 . . . . 5
87bicomi 193 . . . 4
9 trcrm 25054 . . . . . 6
109notbii 287 . . . . 5
11 ax-ltl2 25078 . . . . 5
122notbii 287 . . . . . . 7
131, 12bitr2i 241 . . . . . 6
1413binxt 25087 . . . . 5
1510, 11, 143bitri 262 . . . 4
168, 15anbi12i 678 . . 3
176, 16bitri 240 . 2
181, 5, 173bitri 262 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 176   wo 357   wa 358   wtru 1307  wbox 25073  wdia 25074  wcirc 25075   wunt 25076 This theorem is referenced by:  alneal1  25103  alneal2  25104 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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