Theorem 3adant3r1 1236

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 1228	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	3adantr1 1180	1 ⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

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 1004

This theorem is referenced by:  ccatswrd  11241  imasmnd2  13525  grpsubsub  13662  grpnnncan2  13670  imasgrp2  13687  mulgnn0ass  13735  mulgsubdir  13739  cmn32  13881  ablsubadd  13889  imasrng  13959  imasring  14067  opprrng  14080  opprring  14082  xmettri3  15088  mettri3  15089  xmetrtri  15090  rprelogbmulexp  15670