Theorem bianfi 553

Description: A wff conjoined with falsehood is false.

Hypothesis

Ref	Expression
bianfi.1	⊢ ¬ φ

Assertion

Ref	Expression
bianfi	⊢ (φ ↔ (ψ ∧ φ))

Proof of Theorem bianfi

Step	Hyp	Ref	Expression
1		bianfi.1	. . 3 ⊢ ¬ φ
2	1	pm2.21i 73	. 2 ⊢ (φ → (ψ ∧ φ))
3		pm3.27 260	. 2 ⊢ ((ψ ∧ φ) → φ)
4	2, 3	impbi 139	1 ⊢ (φ ↔ (ψ ∧ φ))

Syntax hints:  ¬ wn 1   ↔ wb 127   ∧ wa 196

This theorem is referenced by:  in0 1722  opthprc 2457

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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