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Mirrors > Home > MPE Home > Th. List > ad5antlr | Structured version Visualization version GIF version |
Description: Deduction adding 5 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad5antlr | ⊢ ((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | ad4antlr 765 | . 2 ⊢ (((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
3 | 2 | adantr 480 | 1 ⊢ ((((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: ad6antlr 769 restmetu 22185 usg2spot2nb 26592 foresf1o 28727 fimaproj 29228 locfinreflem 29235 pstmxmet 29268 mblfinlem3 32618 itg2gt0cn 32635 pell1234qrmulcl 36437 suplesup 38496 limclner 38718 bgoldbtbnd 40225 |
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