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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