This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ceqsexv2dOLD

Description: Obsolete version of ceqsexv2d as of 5-Jun-2025. (Contributed by Thierry Arnoux, 10-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ceqsexv2dOLD.1	$⊢ A \in V$
	ceqsexv2dOLD.2	$⊢ x = A \to (φ \leftrightarrow ψ)$
	ceqsexv2dOLD.3	$⊢ ψ$
Assertion	ceqsexv2dOLD	$⊢ \exists x φ$

Proof

Step	Hyp	Ref	Expression
1		ceqsexv2dOLD.1	$⊢ A \in V$
2		ceqsexv2dOLD.2	$⊢ x = A \to (φ \leftrightarrow ψ)$
3		ceqsexv2dOLD.3	$⊢ ψ$
4	1 2	ceqsexv	$⊢ \exists x (x = A \land φ) \leftrightarrow ψ$
5	4	biimpri	$⊢ ψ \to \exists x (x = A \land φ)$
6		exsimpr	$⊢ \exists x (x = A \land φ) \to \exists x φ$
7	3 5 6	mp2b	$⊢ \exists x φ$