Theorem anandirs 395

Description: Inference that undistributes conjunction in the antecedent.

Hypothesis

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

Assertion

Ref	Expression
anandirs	⊢ (((φ ∧ ψ) ∧ χ) → τ)

Proof of Theorem anandirs

Step	Hyp	Ref	Expression
1		anandirs.1	. . 3 ⊢ (((φ ∧ χ) ∧ (ψ ∧ χ)) → τ)
2	1	an4s 390	. 2 ⊢ (((φ ∧ ψ) ∧ (χ ∧ χ)) → τ)
3	2	anabsan2 387	1 ⊢ (((φ ∧ ψ) ∧ χ) → τ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  3impdir 631  fvreseq 2882  oawordri 3152  phplem5 3407  axrecex 4079  hosclt 5491  hodclt 5492  spansncv 5542  5oalem3 5546  5oalem5 5548  mdsymlem5 5780

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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