Theorem anandirs 597

Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)

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 592	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜒 ∧ 𝜒)) → 𝜏)
3	2	anabsan2 586	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  3impdir  1330  fvreseq  5753  phplem4  7046  muladd  8568  iccshftr  10234  iccshftl  10236  iccdil  10238  icccntr  10240  fzaddel  10299  fzsubel  10300  mulexp  10846  upxp  15025  uptx  15027