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Theorem 3eqtr3i 97
 Description: Transitivity of equality. (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypotheses
Ref Expression
3eqtr4i.1 A:α
3eqtr4i.2 R⊧[A = B]
3eqtr3i.3 R⊧[A = S]
3eqtr3i.4 R⊧[B = T]
Assertion
Ref Expression
3eqtr3i R⊧[S = T]

Proof of Theorem 3eqtr3i
StepHypRef Expression
1 3eqtr4i.1 . 2 A:α
2 3eqtr4i.2 . 2 R⊧[A = B]
3 3eqtr3i.3 . . 3 R⊧[A = S]
41, 3eqcomi 79 . 2 R⊧[S = A]
51, 2eqtypi 78 . . 3 B:α
6 3eqtr3i.4 . . 3 R⊧[B = T]
75, 6eqcomi 79 . 2 R⊧[T = B]
81, 2, 4, 73eqtr4i 96 1 R⊧[S = T]
 Colors of variables: type var term Syntax hints:   = ke 7  [kbr 9  ⊧wffMMJ2 11  wffMMJ2t 12 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  dfan2  154  cbvf  179  leqf  181  axext  219
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