Description: Distribute quantifiers over a nested implication.
This and the following theorems are the general instances of already proved theorems. They could be moved to the main part, before ax-5 . I propose to move to the main part: bj-exalim , bj-exalimi , bj-exalims , bj-exalimsi , bj-ax12i , bj-ax12wlem , bj-ax12w , and remove equs3OLD . A new label is needed for bj-ax12i and label suggestions are welcome for the others. I also propose to change -. A. x -. to E. x in speimfw and spimfw (other spim* theorems use E. x and very few theorems in set.mm use -. A. x -. ). (Contributed by BJ, 8-Nov-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | bj-exalim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.04 | ||
2 | 1 | alimi | |
3 | bj-alexim | ||
4 | pm2.04 | ||
5 | 2 3 4 | 3syl |