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Theorem gstho 491
 Description: "OR" version of Gudder-Schelp's Theorem.
Hypotheses
Ref Expression
gstho.1 b C c
gstho.2 a C (bc)
Assertion
Ref Expression
gstho (ab) C c

Proof of Theorem gstho
StepHypRef Expression
1 anor3 90 . . . 4 (ab ) = (ab)
21ax-r1 35 . . 3 (ab) = (ab )
3 gstho.1 . . . . 5 b C c
43comcom4 455 . . . 4 b C c
5 gstho.2 . . . . . 6 a C (bc)
65comcom4 455 . . . . 5 a C (bc)
7 anor3 90 . . . . . 6 (bc ) = (bc)
87ax-r1 35 . . . . 5 (bc) = (bc )
96, 8cbtr 182 . . . 4 a C (bc )
104, 9gsth2 490 . . 3 (ab ) C c
112, 10bctr 181 . 2 (ab) C c
1211comcom5 458 1 (ab) C c
 Colors of variables: term Syntax hints:   C wc 3  ⊥ wn 4   ∪ 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-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
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