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	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( 𝜓 → ( 𝜒 → 𝜓 ) )
2	1	a1i	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜓 ) ) )