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Theorem 3bitr3ri 267
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 242 . 2 (ψχ)
51, 4bitr3i 242 1 (θχ)
Colors of variables: wff setvar class
Syntax hints:  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  bigolden  901  2eu8  2291  2ralor  2780  sbcco  3068  dfiin2g  4000  nnadjoinpw  4521  el1st  4729  dffun6f  5123  fununi  5160
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