Theorem 3imtr4g

Description: More general version of 3imtr4i . Useful for converting definitions in a formula. (Contributed by NM, 20-May-1996) (Proof shortened by Wolf Lammen, 20-Dec-2013)

	Ref	Expression
Hypotheses	3imtr4g.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	3imtr4g.2	$$⊢\theta \leftrightarrow \psi$$
	3imtr4g.3	$$⊢\tau \leftrightarrow \chi$$
Assertion	3imtr4g	$$⊢\phi \to \left(\theta \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		3imtr4g.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		3imtr4g.2	$$⊢\theta \leftrightarrow \psi$$
3		3imtr4g.3	$$⊢\tau \leftrightarrow \chi$$
4	2 1	biimtrid	$$⊢\phi \to \left(\theta \to \chi \right)$$
5	4 3	imbitrrdi	$$⊢\phi \to \left(\theta \to \tau \right)$$