How to deduce Axiom Schema of Replacement for many parameters?

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I found that there are two versions of Axiom Schema of Replacement.

1.The first one

$\forall \vec{w} \forall A ( (\forall x \in A \exists ! y \varphi(x,y,\vec{w}, A) \implies (\exists B \forall y (y \in B \iff \exists x \in A \varphi(x,y,\vec{w}, A))))$

in which $\vec{w}$ is a vector of parameters, i.e $\vec{w} = (p_{1},p_{2},...,p_{n})$.

2.The second one

$\forall p \forall A ( (\forall x \in A \exists ! y \varphi(x,y,p, A) \implies (\exists B \forall y (y \in B \iff \exists x \in A \varphi(x,y,p, A))))$

in which $p$ is a parameter.

It is quite obvious that we can infer the second from the first.

My question is: Can we deduce the first from the second?

Many thanks for your help!