Metamath Proof Explorer


Theorem efsubd

Description: Difference of exponents law for exponential function, deduction form. (Contributed by SN, 25-Apr-2025)

Ref Expression
Hypotheses efsubd.a φ A
efsubd.b φ B
Assertion efsubd φ e A B = e A e B

Proof

Step Hyp Ref Expression
1 efsubd.a φ A
2 efsubd.b φ B
3 efsub A B e A B = e A e B
4 1 2 3 syl2anc φ e A B = e A e B