Theorem simprd 38

Description: Extract an assumption from the context. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypothesis

Ref	Expression
simpld.1	⊢ R⊧(S, T)

Assertion

Ref	Expression
simprd	⊢ R⊧T

Proof of Theorem simprd

Step	Hyp	Ref	Expression
1		simpld.1	. 2 ⊢ R⊧(S, T)
2	1	ax-cb2 30	. . . 4 ⊢ (S, T):∗
3	2	wctl 33	. . 3 ⊢ S:∗
4	2	wctr 34	. . 3 ⊢ T:∗
5	3, 4	simpr 23	. 2 ⊢ (S, T)⊧T
6	1, 5	syl 16	1 ⊢ R⊧T

Syntax hints:  kct 10  ⊧wffMMJ2 11

This theorem was proved from axioms:  ax-syl 15  ax-simpr 21  ax-cb2 30  ax-wctl 31  ax-wctr 32

This theorem is referenced by:  mpd  156  exmid  199  ax2  204