Theorem 3adant1r 1175

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
3adant1r	⊢ (((φ ∧ τ) ∧ ψ ∧ χ) → θ)

Proof of Theorem 3adant1r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3expb 1152	. . 3 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	2	adantlr 695	. 2 ⊢ (((φ ∧ τ) ∧ (ψ ∧ χ)) → θ)
4	3	3impb 1147	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:  3adant2r  1177  3adant3r  1179  ssfin  4471