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Mirrors > Home > ILE Home > Th. List > 2eximi | GIF version |
Description: Inference adding 2 existential quantifiers to antecedent and consequent. (Contributed by NM, 3-Feb-2005.) |
Ref | Expression |
---|---|
eximi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
2eximi | ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eximi.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | eximi 1564 | . 2 ⊢ (∃𝑦𝜑 → ∃𝑦𝜓) |
3 | 2 | eximi 1564 | 1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1453 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: excomim 1626 cgsex2g 2696 cgsex4g 2697 vtocl2 2715 vtocl3 2716 dtruarb 4085 opelopabsb 4152 mosubopt 4574 xpmlem 4929 brabvv 5785 ssoprab2i 5828 dmaddpqlem 7153 nqpi 7154 dmaddpq 7155 dmmulpq 7156 enq0sym 7208 enq0ref 7209 enq0tr 7210 nq0nn 7218 prarloc 7279 bj-inex 13032 |
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