Can choice function in SHA algorithm be used in a simplied way?

While going through the official documentation SHA algorithms from NIST here.

There is a choice and Majority function used. Maj(𝑥,𝑦,𝑧)=(𝑥∧𝑦)⊕(𝑥∧𝑧)⊕(𝑦∧𝑧)
Ch(𝑥,𝑦,𝑧)=(𝑥∧𝑦)⊕(¬𝑥∧𝑧)

Can I use Ch (or Maj) function in a simplified version?

eg:

(x^y)⊕(¬𝑥∧𝑧)
=(x^y)^ ¬(¬𝑥∧𝑧) + ¬(x^y)^ (¬𝑥∧𝑧)
=(x^y)^(x + ¬z) + (¬x + ¬y)^ (¬𝑥∧𝑧) can be further simplified as

(x^y) + (¬x ^z)

can above simplified version be used ??