Theorem anabss1 381

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabss1.1	⊢ (((φ ∧ ψ) ∧ φ) → χ)

Assertion

Ref	Expression
anabss1	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabss1

Step	Hyp	Ref	Expression
1		anabss1.1	. . 3 ⊢ (((φ ∧ ψ) ∧ φ) → χ)
2	1	adantrr 312	. 2 ⊢ (((φ ∧ ψ) ∧ (φ ∧ ψ)) → χ)
3	2	anidms 332	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  anabss4 383  anabsan 386  ordtri3or 2230  omordi 3164

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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