Theorem 3adant1r 1168

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 1145	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	adantlr 462	. 2 ⊢ (((𝜑 ∧ 𝜏) ∧ (𝜓 ∧ 𝜒)) → 𝜃)
4	3	3impb 1140	1 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 925

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 927

This theorem is referenced by:  3adant2r  1170  3adant3r  1172  tfr1onlembacc  6121  tfr1onlembfn  6123  tfr1onlemaccex  6127  tfr1onlemres  6128  tfrcllembfn  6136  tfrcllemaccex  6140  tfrcllemres  6141  tfrcldm  6142  tfrcl  6143  mulassnqg  7004  prarloc  7123  prmuloc  7186  addasssrg  7363  axaddass  7468