Theorem 3adant3r1 1213

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)

Hypothesis

Ref	Expression
3exp.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
3adant3r1	⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃)

Proof of Theorem 3adant3r1

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3expb 1205	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	3adantr1 1157	1 ⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 979

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 981

This theorem is referenced by:  grpsubsub  12985  grpnnncan2  12993  imasgrp2  13004  mulgnn0ass  13050  mulgsubdir  13054  cmn32  13140  ablsubadd  13148  imasring  13307  opprrng  13320  opprring  13322  xmettri3  14145  mettri3  14146  xmetrtri  14147  rprelogbmulexp  14645