Theorem 3adant3r 1237

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
3adant3r	⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜏)) → 𝜃)

Proof of Theorem 3adant3r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3com13 1210	. . 3 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)
3	2	3adant1r 1233	. 2 ⊢ (((𝜒 ∧ 𝜏) ∧ 𝜓 ∧ 𝜑) → 𝜃)
4	3	3com13 1210	1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜏)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 980

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  df-3an 982

This theorem is referenced by:  addassnqg  7468  mulassnqg  7470  prarloc  7589  ltpopr  7681  ltexprlemfl  7695  ltexprlemfu  7697  addasssrg  7842  axaddass  7958  apmul1  8834  ltmul2  8902  lemul2  8903  dvdscmulr  12004  dvdsmulcr  12005  modremain  12113  ndvdsadd  12115  rpexp12i  12350  xblcntrps  14757  xblcntr  14758