Metamath Proof Explorer


Theorem bj-almp

Description: A quantified form of ax-mp . See also barbara , bj-almpi , and the inference associated with ala1 . (Contributed by BJ, 19-Mar-2026) (Proof modification is discouraged.)

Ref Expression
Hypotheses bj-almp.maj
|- A. x ( ps -> ph )
bj-almp.min
|- A. x ps
Assertion bj-almp
|- A. x ph

Proof

Step Hyp Ref Expression
1 bj-almp.maj
 |-  A. x ( ps -> ph )
2 bj-almp.min
 |-  A. x ps
3 alim
 |-  ( A. x ( ps -> ph ) -> ( A. x ps -> A. x ph ) )
4 1 2 3 mp2
 |-  A. x ph