Theorem bj-equsal1

Description: One direction of equsal . (Contributed by BJ, 30-Sep-2018)

	Ref	Expression
Hypotheses	bj-equsal1.1	$$⊢Ⅎx\psi$$
	bj-equsal1.2	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	bj-equsal1	$$⊢\forall x\left(x=y\to \phi \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-equsal1.1	$$⊢Ⅎx\psi$$
2		bj-equsal1.2	$$⊢x=y\to \left(\phi \to \psi \right)$$
3	2	a2i	$$⊢\left(x=y\to \phi \right)\to \left(x=y\to \psi \right)$$
4	3	alimi	$$⊢\forall x\left(x=y\to \phi \right)\to \forall x\left(x=y\to \psi \right)$$
5	1	bj-equsal1ti	$$⊢\forall x\left(x=y\to \psi \right)\leftrightarrow \psi$$
6	4 5	sylib	$$⊢\forall x\left(x=y\to \phi \right)\to \psi$$