Theorem 2sbiev

Description: Conversion of double implicit substitution to explicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . See 2sbievw for a version with extra disjoint variables, but based on fewer axioms. (Contributed by AV, 29-Jul-2023) (New usage is discouraged.)

	Ref	Expression
Hypothesis	2sbiev.1	|- ( ( x = t /\ y = u ) -> ( ph <-> ps ) )
Assertion	2sbiev	|- ( [ t / x ] [ u / y ] ph <-> ps )

Proof

Step	Hyp	Ref	Expression
1		2sbiev.1	|- ( ( x = t /\ y = u ) -> ( ph <-> ps ) )
2		nfv	|- F/ x ps
3	1	sbiedv	|- ( x = t -> ( [ u / y ] ph <-> ps ) )
4	2 3	sbie	|- ( [ t / x ] [ u / y ] ph <-> ps )