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CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical equivalence
syl5rbb
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Metamath Proof Explorer
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Theorem
syl5rbb
Description:
A syllogism inference from two biconditionals.
(Contributed by
NM
, 1-Aug-1993)
Ref
Expression
Hypotheses
syl5rbb.1
⊢
φ
↔
ψ
syl5rbb.2
⊢
χ
→
ψ
↔
θ
Assertion
syl5rbb
⊢
χ
→
θ
↔
φ
Proof
Step
Hyp
Ref
Expression
1
syl5rbb.1
⊢
φ
↔
ψ
2
syl5rbb.2
⊢
χ
→
ψ
↔
θ
3
1
2
syl5bb
⊢
χ
→
φ
↔
θ
4
3
bicomd
⊢
χ
→
θ
↔
φ