let X, Y, Z be set ; :: thesis: ( X meets Y /\ Z implies X meets Y )

assume X meets Y /\ Z ; :: thesis: X meets Y

then consider x being object such that

A1: x in X and

A2: x in Y /\ Z by XBOOLE_0:3;

x in Y by A2, XBOOLE_0:def 4;

hence X meets Y by A1, XBOOLE_0:3; :: thesis: verum

assume X meets Y /\ Z ; :: thesis: X meets Y

then consider x being object such that

A1: x in X and

A2: x in Y /\ Z by XBOOLE_0:3;

x in Y by A2, XBOOLE_0:def 4;

hence X meets Y by A1, XBOOLE_0:3; :: thesis: verum