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Mirrors > Home > MPE Home > Th. List > ad5ant12 | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) |
Ref | Expression |
---|---|
ad5ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
ad5ant12 | ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad5ant2.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | ad3antrrr 727 | 1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 |
This theorem is referenced by: fpwwe2 10400 swrdccatin1 14436 lo1bdd2 15231 funcpropd 17614 curf2ndf 17963 metcnp3 23694 perpneq 27073 nsgmgc 31593 fmla1 33345 fnchoice 42542 hoidmvle 44109 isomuspgrlem1 45248 |
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