take
T --> (R^1 1)
; :: thesis: ( T --> (R^1 1) is non-empty & T --> (R^1 1) is continuous )

thus ( T --> (R^1 1) is non-empty & T --> (R^1 1) is continuous ) ; :: thesis: verum

thus ( T --> (R^1 1) is non-empty & T --> (R^1 1) is continuous ) ; :: thesis: verum