On the contrary, in an intuitionistic setting you can use https://en.wikipedia.org/wiki/Synthetic_differential_geometr... and https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis which aren't nearly as easy to phrase classically. (Sure you can phrase things in terms of toposes, but that's just a roundabout way of saying that you're operating in a constructive setting.)

Can do it in pure ZF:

https://www.youtube.com/watch?v=YE68yptMMeQ

https://u.cs.biu.ac.il/~katzmik/spot.html