Theorem anabss1 502

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 397	. 2 ⊢ (((φ ⋀ ψ) ⋀ (φ ⋀ ψ)) → χ)
3	2	anidms 437	1 ⊢ ((φ ⋀ ψ) → χ)

Syntax hints:   → wi 3   ⋀ wa 223

This theorem is referenced by:  anabss4 504  anabsan 507  pm5.54 687  ordtri3or 2995  omordi 4213

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain