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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	\|- ( E. y ( y = A /\ ph ) <-> [. A / y ]. ph )

Proof

Step	Hyp	Ref	Expression
1		sbc5	\|- ( [. A / y ]. ph <-> E. y ( y = A /\ ph ) )
2	1	bicomi	\|- ( E. y ( y = A /\ ph ) <-> [. A / y ]. ph )