Theorem sb6rf

Description: Reversed substitution. For a version requiring disjoint variables, but fewer axioms, see sb6rfv . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker sb6rfv if possible. (Contributed by NM, 1-Aug-1993) (Revised by Mario Carneiro, 6-Oct-2016) (Proof shortened by Wolf Lammen, 21-Sep-2018) (New usage is discouraged.)

	Ref	Expression
Hypothesis	sb5rf.1	|- F/ y ph
Assertion	sb6rf	|- ( ph <-> A. y ( y = x -> [ y / x ] ph ) )

Proof

Step	Hyp	Ref	Expression
1		sb5rf.1	|- F/ y ph
2		sbequ12r	|- ( y = x -> ( [ y / x ] ph <-> ph ) )
3	1 2	equsal	|- ( A. y ( y = x -> [ y / x ] ph ) <-> ph )
4	3	bicomi	|- ( ph <-> A. y ( y = x -> [ y / x ] ph ) )