Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rexlimdvaa | GIF version |
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016.) |
Ref | Expression |
---|---|
rexlimdvaa.1 | ⊢ ((𝜑 ∧ (𝑥 ∈ 𝐴 ∧ 𝜓)) → 𝜒) |
Ref | Expression |
---|---|
rexlimdvaa | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexlimdvaa.1 | . . 3 ⊢ ((𝜑 ∧ (𝑥 ∈ 𝐴 ∧ 𝜓)) → 𝜒) | |
2 | 1 | expr 372 | . 2 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → (𝜓 → 𝜒)) |
3 | 2 | rexlimdva 2549 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∈ wcel 1480 ∃wrex 2417 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-ral 2421 df-rex 2422 |
This theorem is referenced by: rexlimddv 2554 nnsucuniel 6391 omp1eomlem 6979 ctmlemr 6993 mulgt0sr 7586 axpre-suploclemres 7709 cnegex 7940 receuap 8430 rexanuz 10760 climcaucn 11120 fsumiun 11246 dvdsval2 11496 prmind2 11801 tgcl 12233 neiint 12314 restopnb 12350 iscnp4 12387 blssexps 12598 blssex 12599 |
Copyright terms: Public domain | W3C validator |