Theorem 3adant3r 1238

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant3r	|- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Proof of Theorem 3adant3r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3com13 1211	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1234	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1211	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  addassnqg  7530  mulassnqg  7532  prarloc  7651  ltpopr  7743  ltexprlemfl  7757  ltexprlemfu  7759  addasssrg  7904  axaddass  8020  apmul1  8896  ltmul2  8964  lemul2  8965  dvdscmulr  12246  dvdsmulcr  12247  modremain  12355  ndvdsadd  12357  rpexp12i  12592  xblcntrps  15000  xblcntr  15001