Theorem chcon1i

Description: Hilbert lattice contraposition law. (Contributed by NM, 15-Jun-2006) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ch0le.1	|- A e. CH
	chjcl.2	|- B e. CH
Assertion	chcon1i	|- ( ( _|_ ` A ) = B <-> ( _|_ ` B ) = A )

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	|- A e. CH
2		chjcl.2	|- B e. CH
3	2 1	chcon2i	|- ( B = ( _|_ ` A ) <-> A = ( _|_ ` B ) )
4		eqcom	|- ( ( _|_ ` A ) = B <-> B = ( _|_ ` A ) )
5		eqcom	|- ( ( _|_ ` B ) = A <-> A = ( _|_ ` B ) )
6	3 4 5	3bitr4i	|- ( ( _|_ ` A ) = B <-> ( _|_ ` B ) = A )