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Theorem 3bitr3ri 200
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
3bitr3i.1 (φψ)
3bitr3i.2 (φχ)
3bitr3i.3 (ψθ)
Assertion
Ref Expression
3bitr3ri (θχ)

Proof of Theorem 3bitr3ri
StepHypRef Expression
1 3bitr3i.3 . 2 (ψθ)
2 3bitr3i.1 . . 3 (φψ)
3 3bitr3i.2 . . 3 (φχ)
42, 3bitr3i 175 . 2 (ψχ)
51, 4bitr3i 175 1 (θχ)
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:  bigolden  848  sb9  1833  sbcco  2758  dfiin2g  3660  dffun6f  4837
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