Theorem pm13.13b

Description: Theorem *13.13 in WhiteheadRussell p. 178 with different variable substitution. (Contributed by Andrew Salmon, 3-Jun-2011)

	Ref	Expression
Assertion	pm13.13b	$$⊢\left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \wedge x=A\right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		sbceq1a	$$⊢x=A\to \left(\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \right)$$
2	1	biimparc	$$⊢\left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \wedge x=A\right)\to \phi$$