Theorem subsym1

Description: A symmetry with [ x / y ] .

See negsym1 for more information. (Contributed by Anthony Hart, 11-Sep-2011)

	Ref	Expression
Assertion	subsym1	|- ( [ y / x ] [ y / x ] F. -> [ y / x ] ph )

Proof

Step	Hyp	Ref	Expression
1		sbv	|- ( [ y / x ] F. <-> F. )
2		falim	|- ( F. -> ph )
3	1 2	sylbi	|- ( [ y / x ] F. -> ph )
4	3	sbimi	|- ( [ y / x ] [ y / x ] F. -> [ y / x ] ph )