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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical equivalence
bitr2di
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Metamath Proof Explorer
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Theorem
bitr2di
Description:
A syllogism inference from two biconditionals.
(Contributed by
NM
, 5-Aug-1993)
Ref
Expression
Hypotheses
bitr2di.1
⊢
φ
→
ψ
↔
χ
bitr2di.2
⊢
χ
↔
θ
Assertion
bitr2di
⊢
φ
→
θ
↔
ψ
Proof
Step
Hyp
Ref
Expression
1
bitr2di.1
⊢
φ
→
ψ
↔
χ
2
bitr2di.2
⊢
χ
↔
θ
3
1
2
bitrdi
⊢
φ
→
ψ
↔
θ
4
3
bicomd
⊢
φ
→
θ
↔
ψ