Theorem bj-a1k

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

	Ref	Expression
Assertion	bj-a1k	|- ( ph -> ( ps -> ( ch -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1	|- ( ps -> ( ch -> ps ) )
2	1	a1i	|- ( ph -> ( ps -> ( ch -> ps ) ) )