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Mirrors > Home > ILE Home > Th. List > syl221anc | Unicode version |
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.) |
Ref | Expression |
---|---|
sylXanc.1 | |
sylXanc.2 | |
sylXanc.3 | |
sylXanc.4 | |
sylXanc.5 | |
syl221anc.6 |
Ref | Expression |
---|---|
syl221anc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylXanc.1 | . 2 | |
2 | sylXanc.2 | . 2 | |
3 | sylXanc.3 | . . 3 | |
4 | sylXanc.4 | . . 3 | |
5 | 3, 4 | jca 304 | . 2 |
6 | sylXanc.5 | . 2 | |
7 | syl221anc.6 | . 2 | |
8 | 1, 2, 5, 6, 7 | syl211anc 1239 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 973 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 975 |
This theorem is referenced by: syl222anc 1249 vtocldf 2781 dmdcanapd 8726 exprecap 10506 xrbdtri 11228 2strbasg 12508 2stropg 12509 cnptoprest 12994 blssps 13182 blss 13183 metequiv2 13251 xmettx 13265 |
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