Theorem anabs7 376

Description: Absorption into embedded conjunct.

Assertion

Ref	Expression
anabs7	⊢ ((ψ ∧ (φ ∧ ψ)) ↔ (φ ∧ ψ))

Proof of Theorem anabs7

Step	Hyp	Ref	Expression
1		pm3.27 260	. 2 ⊢ ((ψ ∧ (φ ∧ ψ)) → (φ ∧ ψ))
2		pm3.27 260	. . 3 ⊢ ((φ ∧ ψ) → ψ)
3		id 9	. . 3 ⊢ ((φ ∧ ψ) → (φ ∧ ψ))
4	2, 3	jca 236	. 2 ⊢ ((φ ∧ ψ) → (ψ ∧ (φ ∧ ψ)))
5	1, 4	impbi 139	1 ⊢ ((ψ ∧ (φ ∧ ψ)) ↔ (φ ∧ ψ))

Syntax hints:   ↔ wb 127   ∧ wa 196

This theorem is referenced by:  suppsr3 4018

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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