Theorem anabsan 386

Description: Absorption of antecedent with conjunction.

Hypothesis

Ref	Expression
anabsan.1	⊢ (((φ ∧ φ) ∧ ψ) → χ)

Assertion

Ref	Expression
anabsan	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsan

Step	Hyp	Ref	Expression
1		anabsan.1	. . 3 ⊢ (((φ ∧ φ) ∧ ψ) → χ)
2	1	an1rs 373	. 2 ⊢ (((φ ∧ ψ) ∧ φ) → χ)
3	2	anabss1 381	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  anandis 394  prlem934b 3932

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

metamath.org