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Theorem eqtr4 834
Description: 4-variable transitive law for equivalence.
Assertion
Ref Expression
eqtr4 (((a == b) ^ (b == c)) ^ (c == d)) =< (a == d)
Proof of Theorem eqtr4
StepHypRef Expression
1 mlaoml 833 . . 3 ((a == b) ^ (b == c)) =< (a == c)
21leran 153 . 2 (((a == b) ^ (b == c)) ^ (c == d)) =< ((a == c) ^ (c == d))
3 mlaoml 833 . 2 ((a == c) ^ (c == d)) =< (a == d)
42, 3letr 137 1 (((a == b) ^ (b == c)) ^ (c == d)) =< (a == d)
Colors of variables: term
Syntax hints:   =< wle 2   == tb 5   ^ 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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  oago3.21x  890
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