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Mirrors > Home > ILE Home > Th. List > 3adant3r1 | GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.) |
Ref | Expression |
---|---|
3exp.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3adant3r1 | ⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exp.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3expb 1206 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
3 | 2 | 3adantr1 1158 | 1 ⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ∧ w3a 980 |
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 982 |
This theorem is referenced by: grpsubsub 13005 grpnnncan2 13013 imasgrp2 13024 mulgnn0ass 13070 mulgsubdir 13074 cmn32 13210 ablsubadd 13218 imasrng 13277 imasring 13381 opprrng 13394 opprring 13396 xmettri3 14277 mettri3 14278 xmetrtri 14279 rprelogbmulexp 14777 |
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