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Metamath Proof Explorer

Theorem pm13.195

Description: Theorem *13.195 in WhiteheadRussell p. 179. This theorem is very similar to sbc5 . (Contributed by Andrew Salmon, 3-Jun-2011) (Revised by NM, 4-Jan-2017)

		Ref	Expression
	Assertion	pm13.195	$⊢ \exists y (y = A \land φ) \leftrightarrow \underset{˙}{[} A / y \underset{˙}{]} φ$

Proof

Step	Hyp	Ref	Expression
1		sbc5	$⊢ \underset{˙}{[} A / y \underset{˙}{]} φ \leftrightarrow \exists y (y = A \land φ)$
2	1	bicomi	$⊢ \exists y (y = A \land φ) \leftrightarrow \underset{˙}{[} A / y \underset{˙}{]} φ$