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)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6

This theorem is referenced by:  dfwe2  7761  ordunisuc2  7828  smo11  8339  r111  9735  2sqnn0  27560  elclnbgrelnbgr  48445  prmringnzring  48957