Metamath Proof Explorer


Theorem chcon1i

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

Ref Expression
Hypotheses ch0le.1 A C
chjcl.2 B C
Assertion chcon1i A = B B = A

Proof

Step Hyp Ref Expression
1 ch0le.1 A C
2 chjcl.2 B C
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