Metamath Proof Explorer


Theorem ifex

Description: Existence of the conditional operator (inference form). (Contributed by NM, 2-Sep-2004)

Ref Expression
Hypotheses ifex.1 A V
ifex.2 B V
Assertion ifex if φ A B V

Proof

Step Hyp Ref Expression
1 ifex.1 A V
2 ifex.2 B V
3 1 2 ifcli if φ A B V