Theorem ax1w 13

Description: Weakening of ax-1 6. As a consequence, its associated inference is an instance (where we allow extra hypotheses) of ax-1 6. Its commuted form is 2a1 29 (but ax1w 13 does not require ax-2 7). (Contributed by BJ, 11-Aug-2020.)

Assertion

Ref	Expression
ax1w	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))

Proof of Theorem ax1w

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜓 → (𝜒 → 𝜓))
2	1	a1i 11	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6

This theorem is used by:  dfwe2  7771  ordunisuc2  7838  smo11  8349  r111  9745  2sqnn0  27613  elclnbgrelnbgr  48618  prmringnzring  49130