Theorem ibir 450

Description: Inference that converts a biconditional implied by one of its arguments, into an implication.

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 399	. 2 ⊢ (φ → (φ ↔ ψ))
3	2	ibi 449	1 ⊢ (φ → ψ)

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  oacl 3138  cdafi 3730  expcllem 4682

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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