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Mirrors > Home > ILE Home > Th. List > r19.27av | Unicode version |
Description: Restricted version of one direction of Theorem 19.27 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by NM, 3-Jun-2004.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
r19.27av |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . . . 4 | |
2 | 1 | ralrimiv 2542 | . . 3 |
3 | 2 | anim2i 340 | . 2 |
4 | r19.26 2596 | . 2 | |
5 | 3, 4 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2141 wral 2448 |
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 1440 ax-gen 1442 ax-4 1503 ax-17 1519 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-ral 2453 |
This theorem is referenced by: r19.28av 2606 fimaxre2 11190 |
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