Theorem bj-a1k

Description: Weakening of ax-1 . As a consequence, its associated inference is an instance (where we allow extra hypotheses) of ax-1 . Its commuted form is 2a1 (but bj-a1k does not require ax-2 ). Shortens dfwe2 (937>925), ordunisuc2 (789>777), r111 (558>545), smo11 (1176>1164). (Contributed by BJ, 11-Aug-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-a1k	$$⊢\phi \to \left(\psi \to \left(\chi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\psi \to \left(\chi \to \psi \right)$$
2	1	a1i	$$⊢\phi \to \left(\psi \to \left(\chi \to \psi \right)\right)$$