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Mirrors > Home > ILE Home > Th. List > 19.8ad | GIF version |
Description: If a wff is true, it is true for at least one instance. Deduction form of 19.8a 1590. (Contributed by DAW, 13-Feb-2017.) |
Ref | Expression |
---|---|
19.8ad.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.8ad | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8ad.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | 19.8a 1590 | . 2 ⊢ (𝜓 → ∃𝑥𝜓) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1492 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: suplocexprlemloc 7698 sgrpidmndm 12700 |
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