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Theorem dp15lemb 1153
Description: Part of proof (1)=>(5) in Day/Pickering 1982.
Hypotheses
Ref Expression
dp15lema.1 d = (a2 v (a0 ^ (a1 v b1)))
dp15lema.2 p0 = ((a1 v b1) ^ (a2 v b2))
dp15lema.3 e = (b0 ^ (a0 v p0))
Assertion
Ref Expression
dp15lemb ((a0 v a1) ^ (e v b1)) =< (((a0 v d) ^ (e v b2)) v ((a1 v d) ^ (b1 v b2)))
Proof of Theorem dp15lemb
StepHypRef Expression
1 dp15lema.1 . . 3 d = (a2 v (a0 ^ (a1 v b1)))
2 dp15lema.2 . . 3 p0 = ((a1 v b1) ^ (a2 v b2))
3 dp15lema.3 . . 3 e = (b0 ^ (a0 v p0))
41, 2, 3dp15lema 1152 . 2 ((a0 v e) ^ (a1 v b1)) =< (d v b2)
54ax-arg 1151 1 ((a0 v a1) ^ (e v b1)) =< (((a0 v d) ^ (e v b2)) v ((a1 v d) ^ (b1 v b2)))
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-ml 1120  ax-arg 1151
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by:  dp15lemc  1154
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