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Theorem ssdifd 3263
Description: If 𝐴 is contained in 𝐵, then (𝐴𝐶) is contained in (𝐵𝐶). Deduction form of ssdif 3262. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
ssdifd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
ssdifd (𝜑 → (𝐴𝐶) ⊆ (𝐵𝐶))

Proof of Theorem ssdifd
StepHypRef Expression
1 ssdifd.1 . 2 (𝜑𝐴𝐵)
2 ssdif 3262 . 2 (𝐴𝐵 → (𝐴𝐶) ⊆ (𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐴𝐶) ⊆ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  cdif 3118  wss 3121
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-in1 609  ax-in2 610  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-dif 3123  df-in 3127  df-ss 3134
This theorem is referenced by:  ssdif2d  3266  phplem4dom  6840  fisseneq  6909
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