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Mirrors > Home > ILE Home > Th. List > ad4antr | GIF version |
Description: Deduction adding 4 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
ad2ant.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
ad4antr | ⊢ (((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad2ant.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | ad3antrrr 461 | . 2 ⊢ ((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓) |
3 | 2 | adantr 261 | 1 ⊢ (((((𝜑 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem is referenced by: ad5antr 465 cauappcvgprlemloc 6750 caucvgprlemm 6766 caucvgprlemladdrl 6776 caucvgprlemlim 6779 caucvgprprlemml 6792 caucvgprprlemexbt 6804 caucvgprprlemlim 6809 caucvgsrlemgt1 6879 axcaucvglemres 6973 rebtwn2zlemstep 9107 caucvgre 9580 cvg1nlemres 9584 resqrexlemglsq 9620 |
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