Theorem ax1w

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 ax1w does not require ax-2 ). (Contributed by BJ, 11-Aug-2020)

	Ref	Expression
Assertion	ax1w	$$⊢\phi \to \left(\psi \to \left(\chi \to \psi \right)\right)$$

Proof

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