Theorem bj-a1k 34651

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 28 (but bj-a1k 34651 does not require ax-2 7). This shortens the proofs of dfwe2 7602 (937>925), ordunisuc2 7666 (789>777), r111 9464 (558>545), smo11 8166 (1176>1164). (Contributed by BJ, 11-Aug-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-a1k	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))

Proof of Theorem bj-a1k

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: (None)