Theorem pm13.193

Description: Theorem *13.193 in WhiteheadRussell p. 179. (Contributed by Andrew Salmon, 3-Jun-2011)

	Ref	Expression
Assertion	pm13.193	$$⊢\left(\phi \wedge x=y\right)\leftrightarrow \left(\left[y/x\right]\phi \wedge x=y\right)$$

Proof

Step	Hyp	Ref	Expression
1		sbequ12	$$⊢x=y\to \left(\phi \leftrightarrow \left[y/x\right]\phi \right)$$
2	1	pm5.32ri	$$⊢\left(\phi \wedge x=y\right)\leftrightarrow \left(\left[y/x\right]\phi \wedge x=y\right)$$