Metamath Proof Explorer


Theorem stdpc4lem

Description: In the case of stdpc4 , rename-sb is derivable from fewer axioms than dfsb . The essential proof step is presented in this lemma. Based on a proof of BJ, 22-Dec-2020. (Contributed by Wolf Lammen, 4-Jun-2026)

Ref Expression
Assertion stdpc4lem
|- ( A. x ph -> A. y ( y = t -> A. x ( x = y -> ph ) ) )

Proof

Step Hyp Ref Expression
1 ala1
 |-  ( A. x ph -> A. x ( x = y -> ph ) )
2 1 a1d
 |-  ( A. x ph -> ( y = t -> A. x ( x = y -> ph ) ) )
3 2 alrimiv
 |-  ( A. x ph -> A. y ( y = t -> A. x ( x = y -> ph ) ) )