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Mirrors > Home > MPE Home > Th. List > syl6c | Structured version Visualization version GIF version |
Description: Inference combining syl6 35 with contraction. (Contributed by Alan Sare, 2-May-2011.) |
Ref | Expression |
---|---|
syl6c.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
syl6c.2 | ⊢ (𝜑 → (𝜓 → 𝜃)) |
syl6c.3 | ⊢ (𝜒 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
syl6c | ⊢ (𝜑 → (𝜓 → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6c.2 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) | |
2 | syl6c.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | syl6c.3 | . . 3 ⊢ (𝜒 → (𝜃 → 𝜏)) | |
4 | 2, 3 | syl6 35 | . 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏))) |
5 | 1, 4 | mpdd 43 | 1 ⊢ (𝜑 → (𝜓 → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: syl6ci 71 syldd 72 impbidd 200 pm5.21ndd 368 jcad 502 zorn2lem6 9523 sqreulem 14300 ontopbas 32757 ontgval 32760 ordtoplem 32764 ordcmp 32776 jaodd 37766 ee33 39245 sb5ALT 39249 tratrb 39264 onfrALTlem2 39279 onfrALT 39282 ax6e2ndeq 39293 ee22an 39416 sspwtrALT 39567 sspwtrALT2 39573 trintALT 39632 |
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