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Theorem ibir 233

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004.)

**Hypothesis**
Ref	Expression
ibir.1	⊢ (φ → (ψ ↔ φ))

**Assertion**
Ref	Expression
ibir	⊢ (φ → ψ)

**Proof of Theorem ibir**
Step	Hyp	Ref	Expression
1		ibir.1	. . 3 ⊢ (φ → (ψ ↔ φ))
2	1	bicomd 192	. 2 ⊢ (φ → (φ ↔ ψ))
3	2	ibi 232	1 ⊢ (φ → ψ)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ↔ wb 176

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177

This theorem is referenced by: elpr2 3752 opkelimagekg 4271 ffdm 5234 ov 5595 enprmaplem6 6081