Theorem 3adant1r 1258

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 1231	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	adantlr 477	. 2 ⊢ (((𝜑 ∧ 𝜏) ∧ (𝜓 ∧ 𝜒)) → 𝜃)
4	3	3impb 1226	1 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1005

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 1007

This theorem is referenced by:  3adant2r  1260  3adant3r  1262  tfr1onlembacc  6573  tfr1onlembfn  6575  tfr1onlemaccex  6579  tfr1onlemres  6580  tfrcllembfn  6588  tfrcllemaccex  6592  tfrcllemres  6593  tfrcldm  6594  tfrcl  6595  mulassnqg  7699  prarloc  7818  prmuloc  7881  addasssrg  8071  axaddass  8187  ghmgrp  13835