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Theorem 3bitr2ri 198
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitr2i.1 (φψ)
3bitr2i.2 (χψ)
3bitr2i.3 (χθ)
Assertion
Ref Expression
3bitr2ri (θφ)

Proof of Theorem 3bitr2ri
StepHypRef Expression
1 3bitr2i.1 . . 3 (φψ)
2 3bitr2i.2 . . 3 (χψ)
31, 2bitr4i 176 . 2 (φχ)
4 3bitr2i.3 . 2 (χθ)
53, 4bitr2i 174 1 (θφ)
Colors of variables: wff set class
Syntax hints:  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  sbnf2  1854  ssrab  3012  rabn0m  3239  unidif0  3911  relop  4429  dmopab3  4491  issref  4650  fununi  4910
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