Theorem bnj133

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj133.1	$$⊢\phi \leftrightarrow \exists x\psi$$
	bnj133.2	$$⊢\chi \leftrightarrow \psi$$
Assertion	bnj133	$$⊢\phi \leftrightarrow \exists x\chi$$

Proof

Step	Hyp	Ref	Expression
1		bnj133.1	$$⊢\phi \leftrightarrow \exists x\psi$$
2		bnj133.2	$$⊢\chi \leftrightarrow \psi$$
3	2	exbii	$$⊢\exists x\chi \leftrightarrow \exists x\psi$$
4	1 3	bitr4i	$$⊢\phi \leftrightarrow \exists x\chi$$