Metamath Proof Explorer


Theorem ifex

Description: Conditional operator existence. (Contributed by NM, 2-Sep-2004)

Ref Expression
Hypotheses ifex.1
|- A e. _V
ifex.2
|- B e. _V
Assertion ifex
|- if ( ph , A , B ) e. _V

Proof

Step Hyp Ref Expression
1 ifex.1
 |-  A e. _V
2 ifex.2
 |-  B e. _V
3 1 2 ifcli
 |-  if ( ph , A , B ) e. _V