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Mirrors > Home > ILE Home > Th. List > ad4antlr | GIF version |
Description: Deduction adding 4 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad4antlr | ⊢ (((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | ad3antlr 493 | . 2 ⊢ ((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
3 | 2 | adantr 276 | 1 ⊢ (((((𝜒 ∧ 𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
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 is referenced by: ad5antlr 497 ctm 7102 suplocexprlemub 7713 suplocexprlemlub 7714 maxabslemval 11201 xrmaxleim 11236 xrmaxiflemval 11242 fsumconst 11446 |
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