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Metamath Proof Explorer

Theorem ifid

Description: Identical true and false arguments in the conditional operator. (Contributed by NM, 18-Apr-2005)

Ref Expression
Assertion ifid ⊢ if φ A A = A

Proof

Step Hyp Ref Expression
1 iftrue ⊢ φ → if φ A A = A
2 iffalse ⊢ ¬ φ → if φ A A = A
3 1 2 pm2.61i ⊢ if φ A A = A