Metamath Proof Explorer


Theorem wl-cbvalsbi

Description: Change bounded variables in a special case. The reverse direction seems to involve ax-11 . My hope is that I will in some future be able to prove mo3 with reversed quantifiers not using ax-11 . See also the remark in mo4 , which lead me to this effort. (Contributed by Wolf Lammen, 5-Mar-2024)

Ref Expression
Assertion wl-cbvalsbi ( ∀ 𝑥 𝜑 → ∀ 𝑦 [ 𝑦 / 𝑥 ] 𝜑 )

Proof

Step Hyp Ref Expression
1 stdpc4 ( ∀ 𝑥 𝜑 → [ 𝑦 / 𝑥 ] 𝜑 )
2 1 alrimiv ( ∀ 𝑥 𝜑 → ∀ 𝑦 [ 𝑦 / 𝑥 ] 𝜑 )