Theorem elimhyps

Description: A version of elimhyp using explicit substitution. (Contributed by NM, 15-Jun-2019)

	Ref	Expression
Hypothesis	elimhyps.1	|- [. B / x ]. ph
Assertion	elimhyps	|- [. if ( ph , x , B ) / x ]. ph

Proof

Step	Hyp	Ref	Expression
1		elimhyps.1	|- [. B / x ]. ph
2		sbceq1a	|- ( x = if ( ph , x , B ) -> ( ph <-> [. if ( ph , x , B ) / x ]. ph ) )
3		dfsbcq	|- ( B = if ( ph , x , B ) -> ( [. B / x ]. ph <-> [. if ( ph , x , B ) / x ]. ph ) )
4	2 3 1	elimhyp	|- [. if ( ph , x , B ) / x ]. ph