Theorem 3adant1r 1231

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 1204	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	adantlr 477	. 2 ⊢ (((𝜑 ∧ 𝜏) ∧ (𝜓 ∧ 𝜒)) → 𝜃)
4	3	3impb 1199	1 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 978

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 980

This theorem is referenced by:  3adant2r  1233  3adant3r  1235  tfr1onlembacc  6345  tfr1onlembfn  6347  tfr1onlemaccex  6351  tfr1onlemres  6352  tfrcllembfn  6360  tfrcllemaccex  6364  tfrcllemres  6365  tfrcldm  6366  tfrcl  6367  mulassnqg  7385  prarloc  7504  prmuloc  7567  addasssrg  7757  axaddass  7873  ghmgrp  12987