Theorem 3adant2l 1176

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	⊢ ((φ ∧ ψ ∧ χ) → θ)

Assertion

Ref	Expression
3adant2l	⊢ ((φ ∧ (τ ∧ ψ) ∧ χ) → θ)

Proof of Theorem 3adant2l

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3com12 1155	. . 3 ⊢ ((ψ ∧ φ ∧ χ) → θ)
3	2	3adant1l 1174	. 2 ⊢ (((τ ∧ ψ) ∧ φ ∧ χ) → θ)
4	3	3com12 1155	1 ⊢ ((φ ∧ (τ ∧ ψ) ∧ χ) → θ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by: (None)