Metamath Proof Explorer

Theorem sylibr

Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by NM, 3-Jan-1993)

Ref Expression
Hypotheses sylibr.1 φ ψ
sylibr.2 χ ψ
Assertion sylibr φ χ


Step Hyp Ref Expression
1 sylibr.1 φ ψ
2 sylibr.2 χ ψ
3 2 biimpri ψ χ
4 1 3 syl φ χ