Theorem 3adant3r 1213

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 1186	. . 3 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)
3	2	3adant1r 1209	. 2 ⊢ (((𝜒 ∧ 𝜏) ∧ 𝜓 ∧ 𝜑) → 𝜃)
4	3	3com13 1186	1 ⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜏)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 962

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

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by:  addassnqg  7183  mulassnqg  7185  prarloc  7304  ltpopr  7396  ltexprlemfl  7410  ltexprlemfu  7412  addasssrg  7557  axaddass  7673  apmul1  8541  ltmul2  8607  lemul2  8608  dvdscmulr  11511  dvdsmulcr  11512  modremain  11615  ndvdsadd  11617  rpexp12i  11822  xblcntrps  12571  xblcntr  12572