- #1
Goldenwind
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Mathematical Logic: "For all" and "There exists"
I need to show that
[tex]\vdash (\forall x)(A \rightarrow (B \equiv C)) \rightarrow ((\forall x)(A \rightarrow B) \equiv (\forall x)(A \rightarrow C))[/tex]
My question to you, how does the [itex](\forall x)[/itex] affect this equation? If they weren't there, I could simply do this question, but their presence is confusing me. What's different? Can I just ignore them and move on as normal?
I need to show that
[tex]\vdash (\forall x)(A \rightarrow (B \equiv C)) \rightarrow ((\forall x)(A \rightarrow B) \equiv (\forall x)(A \rightarrow C))[/tex]
My question to you, how does the [itex](\forall x)[/itex] affect this equation? If they weren't there, I could simply do this question, but their presence is confusing me. What's different? Can I just ignore them and move on as normal?
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