In I Corinthians, Paul was addressing a specific problem that the Church was having. If you will read your footnote on those two verses, you must go back to verse 29 and read from there. The two verses you pulled out support your claim but do not tell the whole story of this passage. Reference I Cor. 11:5, Acts 2:17, 21:9, I Timothy 2:11-12
The early Church was having trouble with false prophets and the two verses you give are specific to that situation. There are many references to women prophesing/teaching and praying in public worship.